In the Raiders' first game in front of spectators in Las Vegas due to past pandemic restrictions, Carr hit Zay Jones with his second TD pass of the night to cap off the comeback victory.
A touchdown from close-range to Josh Jacobs and a 34-yeard field goal to Daniel Carson made it 14-10 at half-time, but Baltimore restored their lead to 17-10 through the only score of the third quarter, a 40-yard field goal to Justin Tucker.
The floodgates then well and truly opened in the fourth, with Las Vegas finding the end zone in the form of Jacobs's second before Baltimore regained the lead through an eight-yard run from Latavius Murray.
A receiving touchdown to Darren Waller again brought the sides level, before each team kicked a late field goal to force extra time.
Carr threw for 435 yards to lead all quarterbacks from week one, while Jackson ran for 86 yards on top of his 235-yard passing effort.