After the Ravens rallied from a nine-point deficit in the fourth quarter to go ahead with 3 ½ minutes remaining, Carr directed a 66-yard drive that ended with a 23-yard strike to Crabtree in the back of the end zone.
Carr went 25 for 35 for 199 yards. Three of his TD passes went to Crabtree, who finished with seven catches for 88 yards to help Oakland (3-1) to its third road win.
The Ravens won their previous three games by excelling in the fourth quarter. This game was a throwback to last year, when Carr pulled out a 37-33 win over Baltimore.
Baltimore was called for offensive holding five times and yielded two sacks.
The Ravens closed to 14-12 with 2:41 left in the third quarter when Flacco bulled in from the 1 to complete a 72-yard drive that consumed seven minutes.
The comeback lost some steam when Bruce Irvin sacked Flacco, forcing a fumble that Oakland recovered on the Baltimore 29.
Copyright 2016 by The Associated Press