Both sides had already qualified for the last 16, but first place was still up for grabs, with the French champions needing just a point at the Camp Nou and Barcelona having to win.
When Zlatan Ibrahimovic put the visitors ahead against his old club on 15 minutes, PSG appeared to be in control, but Barcelona's all-star front line all weighed in with goals to swing the match back the home side's way and ensure that they go through to next Monday's draw as group winners.
Messi equalised just four minutes after Ibrahimovic's opener, before Neymar put the hosts ahead on 42 minutes and Suarez secured the victory 13 minutes from time, ending PSG's record as the last club in Europe's leading leagues still to be unbeaten in all competitions this season.
"We posed them problems but we were not clinical enough," said PSG coach Laurent Blanc, who admitted that his team can now expect a tough draw in the last 16.
"It is a disadvantage to finish second. In a group with FC Barcelona, you can expect to be in a real battle to finish first. We couldn't do it, and now we impatiently await the draw."
Barcelona coach Luis Enrique said: "We have fulfilled our part of the contract by finishing first. And the team that draws us will undoubtedly not be happy."
Barcelona monopolised possession from the start, but PSG took the lead with their first shot on target, Ibrahimovic beating Marc-Andre ter Stegen with a first-time effort on his left-foot after Blaise Matuidi had laid off a Lucas ball in from the right.
It was the Swede's 12th goal of an injury-hit campaign and the first time he had ever scored against Barcelona, the club with whom he spent a year under Pep Guardiola in 2009-10.
However, Barcelona were quickly back level and eventually stole the match.