Forsythe, activated from the 60-day disabled list on Sunday, hammered Steve Edlefsen's 1-0 sinker into the left field bleachers to lift the Padres to their third win in 14 games.
Carlos Quentin went 3-for-4 with a pair of solo shots, including one off Jeremy Affeldt in the eighth to tie it.
Ryan Theriot had three hits and three RBI, but the Giants, fresh off a four- game sweep of the Cubs, lost a game started by Tim Lincecum for the seventh straight time.
"As a starter your job is to put your team in a position to win. Obviously, I haven't been doing that up until now and I'm definitely going to be making that my focal point for the next however many months we have left," said Lincecum.
Lincecum was in line for the victory after Theriot drove in Brandon Crawford with an opposite-field single in the seventh inning.
The Giants had a chance to tack on in the eighth, but Forsythe threw out Angel Pagan trying to go from first to third on Joaquin Arias's base hit in the hole.
Quentin, also recently off the DL, knotted things at 5-5 by golfing his fifth home run to straightaway center.
Huston Street (1-0) worked out of a bases loaded jam in the ninth by getting Buster Posey to ground into a fielder's choice, and Forsythe got the better of Edlefsen (0-1) in the bottom half.
The Giants had been 26-0 when leading after seven innings.
The Padres scored four runs off Lincecum in the fourth, which began with Quentin skying one into the second deck in left field.
"That ball was crushed," Padres manager Bud Black said of Quentin's home run. "That's what we envisioned. We figured he would be a force in the lineup."
Chase Headley doubled and later scored on Everth Cabrera's base hit, while Cameron Maybin doubled into the left-field corner to bring in a pair.
Theriot started San Francisco's comeback in the third with an RBI single, then doubled home Gregor Blanco to jump-start a three-run sixth. Posey and Brandon Belt each knocked in runs with sacrifice flies.
Street was also activated off the DL on Tuesday...Quentin has 15 career multi- home run games...Theriot had four RBI in 29 games coming in...Lincecum struck out eight over six innings and was charged with four runs on five hits and eight walks...San Diego starter Anthony Bass yielded four runs on seven hits in 5 1/3 frames...Pagan went 2-for-4 to extend his hitting streak to 13 games...Blanco had three of the Giants' 13 hits.
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