Goals from Joe Aribo and Kyle Walker-Peters helped Southampton fight back from two goals down to earn a 2-2 draw with Leeds United at St Mary's.
Rodrigo's early second half brace looked to have set Jesse Marsch's side on their way to three points on a stiflingly hot day on the south coast.
But Aribo's first strike for Southampton was followed up by Walker-Peters' second ever Premier League goal ten minutes from time - rescuing a point for Ralph Hasenhuttl's side who had looked down and out after an hour.
Both sides had their opportunities in the first 45 minutes, with Leeds dominating possession, but the game sparked into life - particularly in the goals department - after the interval.
30-year-old Rodrigo, who scored just six goals in 34 Premier League outings last season, opened the scoring for Leeds just a minute after the break, turning home Jack Harrison's cross after Che Adams had carelessly given the ball away in his own half.
Leeds then doubled their lead on the hour - Rodrigo nodding home at the back post after Pascal Struijk's flicked on header from a corner. Southampton, incidentally, decided not to put any defenders on the post, gifting the former Valencia forward acres of space to head beyond Gavin Bazunu.
A change of system for Southampton, which saw forward Sekou Mara introduced for central defender Jan Bednarek, seemed to galvanise Hasenhuttl's side, and they got back to the game through Aribo's first goal for the club.
The £6m signing from Rangers collected Adam Armstrong's low centre and navigated the onrushing Illan Meslier before firing past a host of bodies on the line. But the Saints weren't done there and they bagged a deserved equaliser with ten minutes to go, as Mara's incisive through ball found Walker-Peters. He then fired through Meslier's legs into the far corner - scoring the fifth goal of his entire career.
Leeds were clinging on by the end, with Southampton providing Hasenhuttl with a decent response to their 4-1 mauling at Tottenham Hotspur on the opening day.