The Broncos forced three turnovers and put an end to a four-game losing streak. Denver improved to 7-4 and moved within a half game of division-leading San Diego in the AFC West.
New York lost for the fifth time in six games and slipped two games behind Dallas in the NFC East. The Giants host the Cowboys next week.
Denver built a 16-0 halftime lead, thanks chiefly to field goals of 26, 32 and 47 yards by Matt Prater.
New York cut its deficit to 10 points in the third quarter on a pair of field goals by Lawrence Tynes but Denver took complete control thanks to a 64-yard drive directed by Orton early in the fourth period.
Orton hit Stokley with a 17-yard scoring pass at the end of the march for a 23-6 lead with 10:15 to play. Prater added his fourth field goal with 5:02 remaining.
Orton completed 18-of-28 passes for 245 yards. New York's Eli Manning was 24-of-40 for 230 yards with an interception.
Denver recovered two New York fumbles.
Denver won its first six games this season before suffering consecutive losses to Baltimore, Pittsburgh, Washington and San Diego. The Broncos scored no more than 17 points in any of those setbacks.