Andrei Kostitsyn scored with 1.5 seconds left in the first to draw Montreal even at 1.
R.J. Umberger had a goal and an assist, and Vinny Prospal also scored for Columbus, which had lost three of four.
Sanford made 18 saves in his 10th straight start for the Blue Jackets. The 32-year-old goalie signed with Columbus as a free agent in July after spending the last two seasons in the Canadiens' organization with AHL Hamilton.
Carey Price stopped 26 shots for Montreal, which returned home after a 1-1-1 West Coast trip.
Gionta, who missed half of the second period after he was cut on the face by Blue Jackets defenseman Marc Methot's skate, tapped home a puck in the crease after Tomas Plekanec's centering pass struck former Canadiens defenseman James Wisniewski in front.
Gionta was injured earlier and was down the ice after Methot's leg kicked up and struck him in the face after he checked him into the boards. Gionta had words with the Columbus bench as he went to the dressing room at 11:07. He missed the rest of the period before returning for the start of the third.
Prospal quieted the sold-out crowd just over 2 minutes in when he beat Price for his seventh goal.
Columbus held a 10-7 shots advantage in the first period, but Kostitsyn made the Canadiens' last one count. He drove in and snapped a shot past Sanford for his third goal in four games.
Umberger gave Columbus a 2-1 lead off the ensuing faceoff. He took defenseman Nikita Nikitin's lead pass and drove the left side to beat Price between the pads with a low wrist shot at 11:14.
Price stuck out his left pad to deny Umberger on a breakaway to keep it a one-goal game with less than a minute left in the second after Montreal defenseman P.K. Subban turned over the puck and fell inside the Blue Jackets' blue line.
NOTES: Sanford's only other appearance against the Canadiens was with St. Louis on March 10, 2007. He was pulled after allowing three goals through the first 25:14 of Montreal's 4-3 road win. ... Pacioretty returned after serving a three-game suspension for his hit to the head on Pittsburgh D Kris Letang. ... RW Louis Leblanc, the No. 18 pick by Montreal in the 2009 draft, made his Bell Centre debut after playing his first three NHL games during the Canadiens' trip.