A member of one of the NHL's hottest lines, Forsberg has 28 points in his last 15 games. He got help from winger Milan Hejduk, who also had a goal and assist.
The Avalanche rebounded from Thursday's 4-3 overtime loss to Atlanta and former coach Bob Hartley to improve to 14-1-2-2 in their last 20 contests.
Pittsburgh's Johan Hedberg frustrated Colorado for 40 minutes and the Penguins took a 1-0 lead into the third period on Mario Lemieux's 26th goal 61 seconds into the second.
But Pittsburgh collapsed after Steven Reinprecht drew the Avalanche even 97 seconds into the third.
Just under two minutes later, defenseman Rob Blake delivered the back-breaker, registering a shorthanded goal.
Colorado had just eight shots in the final period but broke it open on the goals by Forsberg and Hejduk.
Joe Sakic, playing his third game since returning from a foot injury, contributed a pair of assists for the Avalanche, who pulled within five points of first-place Vancouver in the Northwest Division.