Uruguayan striker Cavani headed home the winner with just nine minutes left, his 18th goal in all competitions this term, to complete a fine week in which he also scored at Arsenal in their midweek Champions League draw.
Cavani had converted from the penalty spot on the half-hour after Rafael had fouled Thiago Motta but Lyon's Mathieu Valbuena responded soon after the break.
The late winner left PSG celebrating only their second league triumph in 11 visits to Lyon and moved them into third place on 32 points, the same tally as Monaco who thrashed Marseille 4-0 on Saturday.
Both cashed in on Nice's slip on Sunday, which leaves the leaders on 33 points after Alassane Plea's early header was cancelled out by Bastia's Enzo Crivelli in the second half.
Missing the injured Mario Balotelli, Nice took the lead through Plea after 11 minutes before being pegged back by a fierce 20-metre shot from Crivelli on the hour.
Plea should have won it for Nice late on but, after rounding the keeper, crashed his shot against the bar.
(Reporting by Neil Robinson and Ian Chadband; editing by Ken Ferris)
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