The 46-year-old Gillis, who was attempting to become the oldest first-time winner on the PGA Tour in 20 years, sent an approach into the water. Spieth made par for his second win at TPC Deere Run in three years.
Now Spieth heads to the British Open in search of his third consecutive major championship.
Spieth and Gillis both finished the final round at 20-under 264. Zach Johnson and Danny Lee tied for third at 19 under.