Manning, who was 14-of-24 for 161 yards, hit Steve Smith on a 4-yard scoring play and connected with Sinorice Moss on an 18-yarder.
Jacobs scored on a 6-yard run and Lawrence Tynes booted a 26-yard field goal for the Giants (3-0), who scored once in each quarter.
New York's Ahmad Bradshaw rushed for 104 yards.
The Bucs (0-3) were held to 28 yards rushing and quarterback Byron Leftwich completed seven passes for only 22 yards.
2014: NFL Cheerleaders [PHOTOS]
Julius Randle breaks leg during NBA debut