Liverpool needed a stunning equaliser from Luis Diaz to deny a battling Crystal Palace victory at Anfield on Monday night after Darwin Nunez was sent off for a head-butt.
Palace frustrated the Reds with great success and took the lead when Wilfried Zaha raced through to fire in his side's first goal of the season.
Nunez had an unsuccessful night in front of goal and made things tougher for Liverpool when he was sent off for head-butting Joachim Andersen.
However, just four minutes after that red card Diaz brought the hosts with a brilliant run from the wing and shot from distance.
James Milner had the game's first chance inside the opening minute, firing over on the half-volley after Vicente Guaita had punched away Trent Alexander-Arnold's cross.
The pressure became incessant quickly as Harvey Elliott slalomed into the box before having a goal-bound shot blocked, with the move eventually ending when Nunez blazed over at the back post.
Mohamed Salah soon missed a sitter by his own standards as Palace's back three remained resolute, with Andersen and Joel Ward impressing in particular.
That work at the back paid dividends for Patrick Vieira's side as they took a stunning lead through star man Zaha. Eberechi Eze bounced past Fabinho and produced a wonderfully timed pass to unleash the Ivory Coast international, who curled an effort beyond Alisson into the bottom corner.
Palace's counter-attacking intent was clear but they netted with their first shot of the evening, having repelled 11 Reds shots themselves in those opening 34 minutes. They were the next to go close, Zaha again being sent free but this time having his effort diverted away by Alisson.
One last first-half attack from the hosts nearly resulted in an equaliser, but Nunez's bobbled finish bounced back off the post before a foul sent Palace into half time with their noses in front.
The Eagles' grip on the game was strengthened courtesy of a moment of madness from Nunez in the second half. Andersen was aggrieved with an off-the-ball incident and grabbed the Uruguayan, who responded by pushing his forehead into the Dane's face.
Facing more than 30 minutes with a player fewer than the visitors, Liverpool made things a lot easier for themselves by drawing level quickly courtesy of a moment of magic from Diaz.
The winger weaved from the touchline to just outside the box, sending a swerving strike fizzing past Guaita to level things up at 1-1.
That goal gave Liverpool the added boost from the Anfield crowd to stay in the contest and search for a winner despite their disadvantage, though it was Zaha who would have won it for Palace had he not struck the woodwork from close range.
Despite the crowd's backing, Liverpool's attack spluttered in the closing stages and Palace deservedly left Merseyside with their first point of the season. The Reds, meanwhile, have now drawn their opening two Premier League games.
Liverpool vs Crystal Palace player ratings - Premier League
1. Liverpool (4-3-3)
GK: Alisson - 6/10 - Made himself big to deny Zaha, having been beaten earlier in the first half.
RB: Trent Alexander-Arnold - 6/10 - Played a number of his probing passes but the pinpoint crossing wasn't quite there.
CB: Nat Phillips - 5/10 - Just about played Zaha onside as Palace exploited Liverpool's high line for the opener. Looked a little exposed whenever Zaha and Ayew ran at him.
CB: Virgil van Dijk - 6/10 - Composed enough. Didn't have enough pace to catch up with Zaha but put a stop to most of what Palace threw at him.
LB: Andy Robertson - 5/10 - Brought off just after the hour, having not enjoyed much success going forward against Clyne and Ward.
CM: Harvey Elliott - 8/10 - Kept Liverpool's attacks flowing freely while looking like a real threat himself.
CM: Fabinho - 7/10 - Left for dead by Eze for Palace's goal. Needed to be even more alert when the Reds went down to ten players.
CM: James Milner - 7/10 - Might have netted inside the first minute had he not lashed wildly over the top. Rugged in his approach and got an assist for Diaz's strike.
RW: Mohamed Salah - 6/10 - Played a more creative role, laying on a number of chances for his teammates. Not his day in front of goal, hitting the target just once.
ST: Darwin Nunez - 2/10 - Hit over when well placed at the back post early on. Gave Liverpool an aerial presence but was a second or two behind Andersen at times. Reacted when provoked by Andersen and got himself sent off.
LW: Luis Diaz - 9/10 - Buzzed around on the flank, producing turns and always looking for the ball. Booked for a shirt pull. Brought the Reds back into the game with his skill, drive and determination.
SUB: Jordan Henderson (63' for Milner) - 6/10 - Brought his gut-busting leadership to the fore during a tough last 30.
SUB: Joe Gomez (63' for Phillips) - 6/10 - On the bench with a knock but replaced the shaky Phillips and was competent.
SUB: Kostas Tsimikas (63' for Robertson) - 5/10 - Chastised by Klopp for some poor crossing.
SUB: Fabio Carvalho (79' for Elliott) - 6/10 - Nearly grabbed a stunning victory for Liverpool but an effort from distance went wide.
Manager: Jurgen Klopp - 6/10 - Dealt a tough hand with his injured centre backs but couldn't get the forward line firing in the first home game of the season.
2. Crystal Palace (3-4-3)
GK: Vicente Guaita - 7/10 - Took a whack early on but recovered to make some good saves. Booked for time wasting.
CB: Joel Ward - 7/10 - Alert to step in and disrupt some Liverpool attacks.
CB: Joachim Andersen - 8/10 - Constantly got his head to some challenging Liverpool crosses. Was up for the challenge against Nunez - so much so he helped get him sent off.
CB: Marc Guehi - 8/10 - An absolute rock at the back alongside Ward and Andersen. Always quick to sniff out danger and rarely beaten in the air.
RWB: Nathaniel Clyne - 7/10 - Had some help from teammates in defence but looked assured out wide.
CM: Eberechi Eze - 8/10 - His assist for Zaha had a bit of everything; great touch, quick dribbling and a precise pass.
CM: Cheick Doucoure - 6/10 - Held his position well in central midfield, helping starve Liverpool of quality opportunities.
CM: Jeffrey Schlupp - 6/10 - Another hardworking display in central midfield from the versatile Schlupp, recovering and clearing the ball frequently.
LWB: Tyrick Mitchell - 7/10 - A terrific defensive display, making three tackles and interceptions apiece.
ST: Jordan Ayew - 6/10 - Worked hard to give Palace some respite out of possession, though it was his partner up front who was the danger for Palace.
ST: Wilfried Zaha - 8/10 - Showed terrific poise to tuck away the opener. Enjoyed some isolated duels with Phillips and should have put them ahead in the second half.
SUB: Odsonne Eduoard (63' for Ayew) - 6/10 - Fresh legs up front to pressure Liverpool's defence after Ayew's shift.
SUB: Will Hughes (79' for Doucoure) - 6/10 - Provided more decent midfield pressing as Doucoure's replacement.
SUB: Luka Milivojevic (79' for Eze) - 6/10 - Not a like-for-like Eze replacement but made things difficult at the end.
SUB: Chris Richards (79' for Mitchel) - 6/10 - On for his Palace debut and helped secure the point.
SUB: Michael Olise (88' for Schlupp) - N/A - A brief appearance.
Manager: Patrick Vieira - 9/10 - Made his intentions clear by stuffing his defence. His side got their breaks and took advantage with Zaha's strike. Vieira may be disappointed with a point after Nunez's red card but it's a result they would have taken beforehand.