Lavezzi, who joined from Napoli in July, scored either side of halftime to send PSG through and ensure Dynamo cannot now qualify from Group A with one round of matches remaining.
He put PSG ahead just before the break when he finished Zlatan Ibrahimovic's through ball with a deft chip. Yevhen Khacheridi's under-hit back pass early in the second half was snapped up by Blaise Matuidi, who squared to Lavezzi for a simple second.
Second-placed PSG, on 12 points, will now meet leaders Porto in the final game, needing a victory to win the group.
"Our tactics malfunctioned in the first half but we managed to catch up in the second. This is a new pitch for us; we needed some time to adjust to it so our players improved after the restart," PSG coach Carlo Ancelotti told a news conference.
"We strive for victory and our aim is to grab the first place in our group."
The hosts had their chances, Salvatore Sirigu saving well from Oleg Gusev's header before Denys Germash failed to tap in the rebound.
Miguel Veloso threatened with a trademark free-kick that flew inches wide and then Brazilian Dudu, surprisingly featuring in the starting XI, hit a curling shot that also went narrowly wide.
PSG withstood the pressure and went ahead with a delightful goal from Lavezzi who exchanged passes with Ibrahimovic before chipping Maxym Koval.
Dudu forced Sirigu into another good save before PSG doubled their lead on 52 minutes when Lavezzi slotted into an unguarded net following Khacheridi's blunder.
Dynamo, with four points, will take their place in the Europa League.
"Do I have to walk on to the pitch and play against them? It is very hard to win without converting your chances into goals," Dynamo coach Oleg Blokhin told 2+2 TV Channel.
"Paris Saint-Germain, for instance, had three shots on target and scored two unnecessary goals, especially the last one. Anyway, we played with dignity and did not allow Paris Saint-Germain to do what they wanted."
