The Parisiens went a goal down in the sixth minute when Eduardo netted the opener, but the Parc des Princes pair struck to guarantee an away win
The reigning Ligue 1 champions extended their lead at the top of the table to five points, claiming victory on the road after Monaco could only draw 1-1 at Montpellier on Friday.
PSG suffered an early blow as Brazilian striker Eduardo put the hosts ahead after just six minutes with a close-range finish.
However, Laurent Blanc's men responded strongly and were rewarded shortly before half-time when Argentine attacker Lavezzi scored only his third goal of the campaign.
Ajaccio provided strong resistance in the second half, but Matuidi's 74th-minute header completed the turnaround and ended a streak of three games without a win against the Stade Francois Coty outfit.
PSG named the same side that saw off Brest in a midweek Coupe de France tie, while the in-form Eduardo started up front for Ajaccio, who made three changes from their own cup triumph over Quimperle last weekend.
The visitors went close inside the first two minutes as Guillermo Ochoa was forced to tip Zlatan Ibrahimovic's deflected free kick over the bar.
Yet it was Ajaccio who surprisingly struck first, Eduardo tapping home Benjamin Andre's lay-off for his third goal in as many matches following good work down the right from Cedric Hengbart.
PSG responded well and would have levelled had Ochoa not displayed great reflexes to keep out Lavezzi's close-range effort.
Ajaccio continued to create chances, though, with midfielder Johan Cavalli shooting wide on the half-volley as his side pushed for a second.
The Parisiens dictated possession without creating many goalscoring opportunities, although the capital club were unfortunate not to level when Ibrahimovic struck the post with a low free kick just before the half-hour mark.
The pressure from PSG finally told four minutes before the break, Lavezzi finishing off a sweeping move after Ibrahimovic had been played through by an excellent pass from Matuidi.
Blanc's men started the second half the brighter, but Ajaccio proved adept at frustrating their opponents, who found life difficult in the final third.
Lavezzi and midfielder Adrien Rabiot spurned PSG's best chances, before visiting keeper Salvatore Sirigu prevented Eduardo from restoring Ajaccio's advantage.
Ajaccio's valiant effort was to prove in vain, though, as a diving Matuidi headed into the bottom corner after Ibrahimovic had turned Javier Pastore's far-post cross back across goal.
Eduardo wasted a chance to equalise for the hosts when he fired into the side-netting with the goal gaping seven minutes from time, before Ochoa prevented Edinson Cavani from adding a brilliant third in stoppage-time.