He also passed Joe DiMaggio for second place in franchise history with 14 grand slams as a Yankee.
"I'm a huge fan of Lou Gehrig, everything he's done," Rodriguez said. "He's become like the gold standard for a Yankee. It's a special moment. I'll think about it someday."
Rodriguez's blast came after shortstop Brendan Ryan, catcher J.R. Murphy and right fielder Ichiro Suzuki reached against Giants' starter Tim Lincecum. Kontos relieved Lincecum, and Rodriguez took a 2-1 fastball from the right-hander and deposited it over the wall in right field.
It was his first grand slam since June 12, 2012, against the Braves in Atlanta, when he tied Gehrig's mark of 23 with a shot off left-hander Jonny Venters. Rodriguez ranks fifth in Major League history with 654 home runs, six behind Willie Mays' mark of 660.
"It's an unbelievable accomplishment," manager Joe Girardi. "And it's a big one for us. To be able to have that many opportunities says that you've been around a long time. But to be able to come through that many times means you've been a powerful hitter for a long time, and that's what he's been."
The grand slam broke an 0-for-14 streak, and it was just his second hit in his last 26 at-bats. Over 40 games this season, Rodriguez is batting .261 with seven home runs and 18 RBIs.
"I was just looking for a ball right down the middle and put a good swing on it. I didn't want to miss the ball," Rodriguez said. "I've been putting a lot of good swings and just popping them straight up. Very frustrating. The swings have been good, I've just been popping them straight up, and I just wanted to make sure I stayed on top of that ball a little bit better."
Rodriguez has been limited to the designated hitter role for his past nine games after leaving a Sept. 11 game with left hamstring tightness and leaving Sunday's game with a tight right calf.
He said his legs are "getting better," though, and he said he's been able to run before the last few games. Rodriguez said he took ground balls on Thursday and plans to talk to Girardi in the next day or two about possibly playing third base.
Girardi said he thought Rodriguez was running better Friday than he had been, but wasn't forthcoming about when the 38-year-old might play the field again.
"When I saw him run to first today, I thought it was the best I had seen him run in a while," Girardi said. "It didn't look like there was any hindrance. It looked like he was able to run pretty freely. I was like, 'Hmm, that looks different than what I've seen in the past few days.'"
The Yankees still have work to do to make up the necessary ground and earn a Wild Card berth, but Rodriguez's record-setting grand slam gave New York a much needed win over San Francisco on Friday.
"That's baseball," Rodriguez said. "One swing can turn a lot of things around."