With the win, the AFC West team take their record to 3-2, while Chicago also fall to a 3-2 start.
After both teams stalled on their opening drives, it was Raiders running back Jacobs who scored the first touchdown of the game, rushing in from 12 yards.
The Bears were looking for a swift response, but quarterback Chase Daniel threw an interception moments later.
He tried to force his pass to tight end Trey Burton but it was picked off by Nicholas Morrow, who took it to Chicago's 24-yard line.
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With Oakland back in possession, a defensive penalty moved the ball to the three-yard line and running back DeAndre Washington punched it in to extend the lead to 14-0.
Daniel failed to get his offense moving in the first half and he was sacked twice early in the game. His third drive ended with another punt, handing the ball back to Oakland eight minutes before half-time.
It was a different story for Derek Carr who was finding his rhythm early, completing passes to Washington, Derek Carrier and Trevor Davis.
A 15-yard penalty cost the Raiders a shot at a third touchdown though, with Daniel Carlson kicking a 41-yard field goal less than two minutes before the break.
Daniel failed to muster any comeback in the remaining moments, as Oakland took a 17-0 lead to the locker rooms at half-time.
Things got much better for the Bears early in the third, with former Raider Khalil Mack recovering a fumble to give his team perfect starting position on their opponents 14-yard line.
David Montgomery finally got Chicago on the scoreboard shortly after, rushing in for a touchdown from two yards.
With the London crowd behind the Bears, Carr's next drive fizzled out at his own 36-yard line, forcing the Raiders to punt once again.
Quarterback Daniel was finally rolling mid-way through the third, driving his team all the way from the 11 to finish in the endzone.
Anthony Miller's 32-yard catch was the highlight of the drive, which ended with Allen Robinson catching a 4-yard pass to make it 17-14 after the extra point.
All of a sudden, a Chicago comeback was on the cards.
In a reverse of the first half, it was Carr who struggled after the break. Another three and out led the Raiders to punt and Tarik Cohen returned it with a monster 71-yard run to the Oakland 16.
Robinson then caught his second touchdown of the evening to swing the game in favour of the Bears 21-17 heading into the fourth.
The Raiders weren't done yet though and started their next drive with good field position thanks to Trevor Davis' 52-yard kick return.
But they couldn't make it count as Prince Amukamara forced Davis to fumble less than a yard from the endzone. It was recovered by the Bears, who started their next drive on the 1.
After almost five minutes in possession, the Bears were forced to punt again, as Oakland started on their next drive on the 3-yard line.
A fake punt saw them pick up enough on fourth down to avoid going three and out again before Carr completed a big pass to Foster Moreau to take his side over the halfway line.
Moreau then made another important catch to move the Raiders to the two-yard line, inside the two-minute warning.
Jacobs finished the drive by punching in his second rushing TD of the night to make it 24-21 after the PAT.
That left Chicago chasing the game with less than two minutes on the clock.
Under pressure, Daniel faltered again, throwing another interception. This time, he was picked off by Gareon Conley.
The Raiders were able to run the clock down, leaving just 13 seconds for the final drive. Daniel couldn't pull off the miracle and Oakland picked up the win in London, 24-21.News Now - Sport News