Landon Collins and Dominique Rodgers-Cromartie each had two interceptions of Keenum, fueling a strong defensive effort in the Giants' 17-10 win over the Rams on Sunday at Twickenham Stadium in London.
Collins returned his first interception for a highlight-reel 44-yard touchdown. His second pick set up Rashard Jennings' go-ahead touchdown run in the fourth quarter.
Both of Rodgers-Cromartie's picks came in the end zone in the fourth quarter, including on the Rams' final drive.
Keenum led the Rams into Giants' territory in the final two minutes. They were at the New York 15-yard line with one minute left, before a miscommunication between Keenum and receiver Brian Quick resulted in Cromartie's second interception in the end zone.
"(Takeaways) usually come in bunches," New York coach Ben McAddo said. "Today was the day."
New York also sacked Keenum three times, held running back Todd Gurley in check and handed the Rams (3-4) their third straight loss.
"Very disappointed," Rams coach Jeff Fisher said. "We've got a long trip back and a week off. We're going to go back to work."
Even with the win, it has been an ugly week for the Giants and the NFL. Both are facing a firestorm of criticism over the handling of the domestic abuse allegations against Giants kicker Josh Brown, who was placed on the commissioner's exempt list Friday. Brown, who admitted to years of abusive behavior toward his ex-wife in newly released police documents, did not make the trip to London and his days in the NFL could be over.
McAdoo said the front office had asked him to focus on the game and that the team would deal with the controversy surrounding Brown when they return to New York.
Veteran Robbie Gould was signed this week and handled the kicking duties Sunday. Gould hit a 29-yard field goal in the first half.
The Rams jumped out a 10-0 lead in the first quarter, with Keenum hooking up with Tavon Austin on a 10-yard touchdown pass.
But Collins jumpstarted the Giants in the second quarter, picking off a tipped pass and weaving his way back and forth across the field for a touchdown that tied the score 10-10 with 7:31 left in the first half.
"Tremendous effort by Landon," McAdoo said. "He looked like a running back. For him to be able to tuck the ball away and push the pile into the end zone, shows a lot. He shows up all over the field. He's a very productive young player. He's a tremendous tackler, which I don't think he gets enough credit for, and he's getting better playing the ball. You saw that tonight."
Giants quarterback Eli Manning, who has never lost to the Rams, completed 24 of 37 passes for 196 yards. He did not throw a touchdown or an interception. Odell Beckham Jr. had five catches for 49 yards.
Keenum finished 32 of 53 for 291 yards with a touchdown and the four interceptions.
The Rams head into their bye week with many questions, including whether it's time to give the No. 1 overall pick, quarterback Jared Goff his shot to start. Fisher said after the game that he was sticking with Kennum, though, and would make changes at receiver before quarterback.
"Take a look at the tape, see who's responsible for the interceptions," said Fisher, who became the third coach in NFL history to lose 150 games. "Quarterback was not the reason we lost."
Gurley was held to 57 yards on 15 carries.
It was a crucial game for both teams. The Giants began the day two games back in the loss column of the first-place Dallas Cowboys in the NFC East. Likewise, the Rams also started the weekend two games behind the first-place Seattle Seahawks in the NFC West.
"We just keep fighting and fighting, so that says a lot about us as a team," Rodgers-Cromartie said. "We're a resilient group."
NOTES: Sunday's game was the first sport other than rugby to be played at Twickenham Stadium. ... The Giants have defeated the Rams eight straight times. ... Giants special teams star Dwayne Harris was injured right before the end of the first and had to be assisted off the field. Harris did return from what the Giants called a lower-back injury. ... The Cincinnati Bengals will play the Washington Redskins next week at Wembley Stadium in London, the last of three games played in the United Kingdom this season.