Trailing 6-5 and down to their last out, Aaron Rowand hit a game-tying home run for the Giants (15-10) to send the game into extra innings where they scored three times in the 12th.
"That was a crazy game," Huff told reporters. "It was a back-and-forth battle. We stayed in it till the last out."
San Francisco ace Tim Lincecum struck out 13 batters in seven innings as he was looking to improve to 5-0 on the season but settled for the no-decision.
"The starter's job isn't to go out and get a win -- it's to put the team in a position to get a win," Lincecum said. "I threw my seven innings, and we nitpicked and scored some big runs when we needed to and it turned into a really exciting game."
The two-time Cy Young winner had a 3-0 lead before allowing a three-run home run to Florida's Hanley Ramirez in the sixth.
The Marlins were shooting for their third win in a row but had a let-down from their bullpen after starter Anibal Sanchez exited having allowed three runs in six innings.
Florida reliever Leo Nunez surrendered the game-tying blast in the ninth before Burke Badenhop allowed the three runs in the 12th.
San Francisco finished with 15 hits on the day. Rowand helped give the club the early lead with a pair of RBI singles and went 3-for-5.
Left-hander Dan Runzler was credited with the win after pitching the 11th for the Giants while Guillermo Mota took care of the final inning for the save.
The talent-packed Giants pitching staff totaled 20 strikeouts, tied for the second most in franchise history.
(Writing by Jahmal Corner in Los Angeles; Editing by Alastair Himmer)