Brazilian Lucas Moura set up both goals with league top scorer Ibrahimovic netting his 18th of the season before the hour mark and Alex scoring with a deft half-volley from a corner two minutes from time as PSG moved to 54 points from 23 games.
Monaco, who visit mid-table Lorient on Saturday and will host champions PSG next week, have 48 points.
France midfielder Cabaye hit the post with a header having made his debut as a substitute in the 67th minute, having joined PSG from Newcastle United on Wednesday for a fee put at 25 million euros ($33.71 million) by local media.
The evening had started with the fans cheering Cabaye but a dominant PSG were booed at the break after failing to create any
clear-cut chances with Bordeaux having defended well.
The hosts were eventually rewarded for their efforts when Ibrahimovic tapped the ball into the net from close range following Moura's precise low cross from the right.
Cabaye, 28, replaced Javier Pastore late on and soon settled into his midfield role, going close to scoring from an Ezequiel Lavezzi cross only to see his effort hit the woodwork.
PSG made it 2-0 a minute later when central defender Alex popped up in the area to turn Moura's corner into the net.
($1 = 0.7415 euros)
(Reporting by Gregory Blachier; Editing by Ken Ferris)
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