After a goalless first half at the Parc des Princes, Angel Di Maria gave PSG the lead in the 56th minute.
After a goalless first half at the Parc des Princes, Angel Di Maria gave PSG the lead in the 56th minute before Cavani doubled the advantage on the hour mark.
The Uruguayan struck again with 20 minutes left, his 29th goal in 29 league appearances this season also his 42nd goal in all competitions, a remarkable total.
Blaise Matuidi then sealed a comfortable victory for Unai Emery's side on a glorious spring evening in the French capital, and Paris climb back above Nice into second place in Ligue 1, three points behind leaders Monaco with seven matches remaining.
"We didn't do enough in the first half and Guingamp don't make it easy but once we got the first goal the game opened up a bit and we went looking for more goals. We are certainly happier with the second half," said Emery.
Nice, who are a further point behind PSG in third but have played a game more, came from behind to win 2-1 at Lille on Friday thanks to a Mario Balotelli double while Radamel Falcao's goal gave Monaco a 1-0 win at Angers on Saturday.
Monaco now go to Germany to face Borussia Dortmund in the first leg of their Champions League quarter-final on Tuesday, while PSG are still recovering from the trauma of their European exit at the hands of Barcelona last month.
They are still in contention to win a clean sweep of the domestic honours for a third season running, however, with the League Cup already in the bag after last week's 4-1 win over Monaco in the final in Lyon.
Guingamp, the modest mid-table club from Brittany who like PSG are into the semi-finals of the French Cup, are the last French team to have beaten the capital side.
However, PSG had gone 19 domestic games without losing since their 2-1 loss in Guingamp in December and Antoine Kombouare's men had not won in 10 away league outings since October.
They started well enough but PSG had the best chances in the first half, Cavani heading against the bar from a Di Maria corner and the Argentine then setting up skipper Blaise Matuidi for a shot that was saved by Guingamp's Swedish goalkeeper Karl-Johan Johnsson.
The home side lost left-back Layvin Kurzawa to injury just before the interval, but they took the lead 11 minutes into the second period.
Cavani picked up possession wide on the left and spotted Di Maria in space in the middle. His pass was perfect and the former Manchester United man controlled the ball before deftly lifting it over the advancing Johnsson.
Four minutes later it was 2-0, Adrien Rabiot releasing Cavani, who got the break of the ball in the box before finishing.
That goal, though, was really all about an outrageous backheel in midfield from Marco Verratti that set Rabiot away in the build-up.
Cavani missed a host of chances to increase the lead before he did make it 3-0, controlling a Di Maria ball forward and advancing into the area where he planted a shot into the bottom-left corner.
Matuidi then completed the scoring in the second minute of stoppage time, bundling in a low cross from the right by substitute Lucas Moura.
Elsewhere in France on Sunday, Marseille's prospects of European qualification took a hit as they were held to a 0-0 draw at Toulouse and Saint-Etienne's own European prospects were not helped as they drew 1-1 at home to Nantes.