Jones gained 108 yards on 16 carries as the game's leading rusher. He completed 29 of 45 passes for 305 yards for Duke (2-0).
Northwestern (1-1) entered the matchup with a three-game winning streak in the series.
Duke's Mark Gilbert intercepted two Clayton Thorson passes. Thorson completed only 11 of 29 passes for 120 yards.
Jones had scoring passes on a 52-yard strike to receiver Chris Taylor and on a 1-yard touchdown toss to tight end Davis Koppenhaver in the third quarter.
Northwestern used Justin Jackson's 5-yard touchdown run after a Duke fumble to cut the lead to 21-10 with 33 seconds left in the first half.
Earlier, Northwestern opened the scoring on Charlie Kuhbander's 40-yard field goal.
Jones had a string of 202 passes without an interception until Montre Hartage's picked him off in the first quarter. Jones was four throws short of the school record.
Jones appeared to be picked off again on the next possession near the goal line, but a targeting call on Northwestern's Jared McGee negated the play. The Blue Devils took advantage, with Jones scoring on an 11-yard run.
Shaun Wilson added an 8-yard touchdown run in the fourth quarter for Duke, which is 2-0 for the fourth time in a five-year span and won't leave its home state until October.
Duke's Austin Parker kicked field goals of 31 and 24 yards in the second half.
Until Riley Lees' 20-yard touchdown reception from Matt Alviti with 2:50 left, Duke hadn't allowed a second-half point in two games this season.