The Cardinals took a 25-24 lead when Ryan Lindley hit Thomas with a 13-yard scoring pass and Andre Ellington ran in a two-point conversion with 5:28 to play.
Denver's last hope disappeared when the Broncos failed on a fourth-down play from their own 20-yard line, giving Arizona a short field. The Cardinals took advantage of it when Taylor ran 15 yards for a touchdown with 1:23 to go.
Lindley completed 17-of-29 passes for 219 yards and two touchdowns. His other scoring throw was of 55 yards to Jaron Brown in the third quarter.
Denver's Zac Dysert went 9-of-20 for 163 yards and found Gerell Robinson with a 25-yard touchdown in the third.
Arizona wound up with a 3-1 mark in exhibition action and Denver closed out the preseason at 2-2.
Denver will play in the first game of the NFL's regular season next Thursday when it hosts defending Super Bowl champion Baltimore. Arizona will visit St. Louis to begin the year on Sept. 8.