Lavezzi gave PSG the lead against the run of play with a fine goal on the stroke of half-time and then made it 2-0 seven minutes after the re-start following a costly error by Dynamo defender Yevhen Khacheridi.
That was enough to secure PSG a top-two finish and they are still battling leaders Porto for first place in Group A, with one point separating the two.
Dynamo needed a win to keep alive their hopes of a place in the knockout stages while PSG only required a draw, and that was evident by the way the Ukrainian side took the game to their opponents in the first half.
Alex missed a good chance for the visitors early on but then Dynamo started to put PSG goalkeeper Salvatore Sirigu in their sights.
Sirigu should really have been picking the ball out of the back of his net in the 25th minute though when, after he had done well to push out a Gusev header from on his line, Denys Garmash was left with a virtual open goal to aim at, but he incredibly smashed the ball wide from six yards out.
Zlatan Ibrahimovic tested Maksym Koval at the other end before Dynamo were back on the attack with Miguel curling a 30-yard free-kick inches wide before Dudu also saw an effort go not far from inside the area.
Dynamo could not find the breakthrough though and they were hit on the stroke of half-time by a rapid PSG counter-attack which Lavezzi finished off.
The Argentina international launched the attack himself from inside his own half before playing the ball out to Ibrahimovic on the right and continuing his charge down the centre. Ibrahimovic's return ball was perfectly weighted for Lavezzi to run onto before cleverly dinking the ball over the diving Koval.
That was a huge blow to Dynamo, but worse was to follow at the start of the second half when they gifted PSG a second goal - from which there was no way back. Khacheridi's attempted back-pass to his keeper from inside his own area was woefully under-hit and Blaise Matuidi got there before Koval and poked the ball inside to Lavezzi, who tapped into an empty net.
Dynamo needed a quick response and they almost got it in the 57th minute when Dudu's deflected shot looked to be looping inside the far post, but Sirigu did superbly to back-peddle and claw the ball away for a corner.
Dynamo would not come any closer than that in the remainder of the match as they had to settle for a place in the Europa League.
|Dynamo Kyiv||Team Statistics||Paris Saint Germain|
|0||1st Half Goals||1|
|5||Shots on Target||3|
|8||Shots off Target||2|
|51||1st Half Poss.||49|
|52.9||2nd Half Poss.||47.1|