City welcomed David Silva back into the starting lineup, with the Spaniard having missed their last two matches for the birth of his daughter. Vincent Kompany also returned to the fold, reclaiming his place as a starter after recovering from his muscular problem.
And as expected, the home side dominated the early going, keeping 81% of the possession in the opening 15 minutes.
Nicolas Otamendi forced Asmir Begovic into a quality save with a powerful shot from distance in the 25th minute, but the Cherries' net bulged just a minute later after the keeper's botched clearance fell to a City boot.
The error led to Fernandinho setting Sergio Aguero up with an unmarked header, and the Argentinian dove low to put it past the ex-Chelsea stopper and put City up 1-0.
City went into halftime with their slim lead intact. But they probably wouldn't have even been ahead if Bournemouth didn't cause their own problems, as Eddie Howe's men did well to keep their chances limited heading into the break.
In-form Raheem Sterling was up to his usual tricks, and gave the home side a two-goal cushion in the the second half, though. Silva played a ball to Aguero, who flicked into Sterling's path without even looking. The England international simply smashed it past Begovic, strengthening City's lead and taking his league tally to 12 for the season.
It would not stop there, however, with Aguero popping up with a second on 80 minutes, heading Bernardo Silva's pinpoint cross into the Bournemouth net to take the lead to 3-0.
Danilo, having come on as a late sub, got in on the December festivities as well, scoring his first goal for City from Sterling's pass after the Englishman played him through on the left side with six minutes left in regulation time.
The Etihad side would have three extra minutes after the 90 within which to score a fifth, but that would be it for Pep Guardiola's men, who put on quite the contrasting show in the second period, having looked subdued in the first.
City have now won 17 straight games after drawing with Everton early in the season. They certainly don't look like anyone can catch them now.
Bench: Bravo, Mangala, Danilo, Touré, Gundogan, Bernardo, Jesus
Bournemouth: Begovic; Smith, Cook, Aké, Simpson, Fraser; Stanislas, Gosling, Surman, Ibe; Wilson
Substitutes: Boruc, Mahoney, Hyndman, Cook, Pugh, Mousset, Afobe