The Argentina international, Ángel Di Maria, showed his class with one sublime and another clinical finish as PSG moved level on points with Monaco at the top of the Ligue 1 table.
PSG press as Monaco juggle priorities
"We are happy because it was a difficult match at Angers," said PSG coach Unai Emery. "We're content with three points. We were well-prepared, concentrated and worked well."
Monaco can reclaim their three-point advantage with victory at home to relegation threatened Dijon on Saturday but with one eye on next week's Champions League quarter-final second leg against Borussia Dortmund, they could be vulnerable.
What's more, Monaco have had one less day to prepare for Saturday's game after their first leg in Germany, which the Principality outfit won 3-2, was postponed 24 hours after a triple bomb blast damaged the home side's team bus and left Spanish defender Marc Bartra with a broken wrist.
How much that incident has affected Monaco's already weary players remains to be seen while PSG - knocked out of Europe themselves in dramatic circumstances in the previous round when Barcelona came back from a 4-0 first leg deficit to triumph 6-5 on aggregate - have only domestic matters to concentrate on now.
Ángel quality the difference over Angers
Di Maria's first goal was a rare bright spark in an otherwise tight first half, but there was no doubting the quality of the Argentine's placement as he bent a sumptuous free-kick from 25 yards over the defensive wall and beyond the despairing reach of Alexandre Letellier in the Angers goal on 28 minutes.
The home side had the ball in the net on 39 minutes through captain Cheikh Ndoye but it was controversially disallowed for a foul by Famara Diedhiou on Serge Aurier when television replays proved inconclusive as to which of the two was the true offender as they wrestled in the area.
Angers make it tough for PSG
Ndoye came close again 18 minutes from time when his powerful header appeared destined for the top corner until goalkeeper Kevin Trapp acrobatically tipped the ball over the bar. For a team in mid-table safety, Angers were playing with real purpose but lacked the quality to break down a stubborn away defence.
And six minutes form time, PSG struck with rapier speed and efficiency on the counter-attack as Lucas Moura fed Di Maria to slot home his second at the near post, although Letellier's positioning was highly questionable.