The Giants (3-2) erased an early 14-0 deficit, scoring 20 consecutive points en route to the victory.
Ahmad Bradshaw rambled for career-high 200 yards and a touchdown on 30 carries. He and Cruz each converted an interception by safety Stevie Brown into a second-quarter touchdown.
Manning finished 25-of-37 through the air for 259 yards with a pick-off as the Giants racked up 502 yards of total offense.
Brandon Weeden hooked up with fellow rookie Josh Gordon on a pair of TD passes but was intercepted twice in the loss, which sent the Browns to 0-5 for the first time since 1999.
Trent Richardson picked up 81 rushing yards and a touchdown on 17 carries for Cleveland.