Sanchez managed to complete only 10-of-21 passes for 97 yards and was intercepted three times in the first half before being benched for the first time this season.
McElroy -- subbing for injured Jets backup quarterback Tim Tebow -- entered and went 5-of-7 through the air for 29 yards, including a 1-yard scoring toss to Cumberland early in the fourth quarter.
The throw enabled the Jets (5-7) to rebound from a one-sided loss to New England last week.
Arizona's Ryan Lindley also had a poor outing, managing just 10-of-31 passing efficiency for 72 yards with an interception for the Cardinals (4-8), who dropped their eighth straight.
Swim Week Miami Beach 2014 [PHOTOS]