Gostkowski put the Patriots on the board with a 30-yard field goal.
The Ravens were first to get a touchdown, in the second quarter, on a 13-play drive during which they faced third down only once, and converted that with a pass to tight end Dennis Pitta.
A few plays later, Flacco got his team into the red zone with a 25-yard connection to Torrey Smith. Smith was covered by Kyle Arrington after Aqib Talib had to leave the game in the first quarter with what the team called a thigh injury.
Ray Rice, who was held to just 31 yards on nine first-half carries, ran the ball in from 2 yards.
Baltimore had started that drive from its 10; being deep in their own half of the field was a familiar spot for the Ravens: their five possessions started inside the 15.
Welker scored with just over four minutes remaining in the half on a 1-yard pass from Brady.