Jacobs, a 264-pound, three-year veteran finished with 54 yards on 11 carries. He also caught four balls for 49 yards.
Tynes nailed field goals of 28, 46 and 20 yards.
Quarterback Eli Manning went 28-for-39 passing for 283 yards as the Giants won for the seventh time in their last eight games. They handed Detroit its first home loss this season.
They led 10-0 at the half and quelled a second-half Detroit rally attempt.
Detroit's Jon Kitna was 28 for 43 for 377 yards, one touchdown and three interceptions.
Newly converted Giants linebacker Mathias Kiwanuka was lost on the second play of the game with a broken left leg.