Spieth improved on the two-under 70 which had allowed Wallace to close out Saturday at 12 under alongside him as joint leader, mixing seven birdies with a bogey on the San Antonio course to finish 18 under for the tournament.
Former winner Hoffman's flawless 66 dragged him to within one of Spieth with two holes to play, but the one-time Masters champion kept his cool to birdie 17 and close out his first PGA Tour triumph since the 2017 Open.
Spieth told the PGA Tour: "I felt really light. I just wanted to come out and smile and have some fun.
"That's been kind of a challenge for me on these Sundays when I've been in contention, I've not come out with a real lightness to me and today I did.
"It's been a long road. I never really doubted myself that I'd get back to where I wanted to go but when you lose confidence a lot of times it's hard to see the positives going forward and I just kept my head down."
Hillingdon-born Wallace's momentum stalled with a bogey on the par-five fourth and he was left to regret what might have been after picking up two late shots across the last three holes.
Lucas Glover also shot 66 to finish fourth, with Anirban Lahiri fifth on 10 under and Patton Kizzire shooting up the leaderboard with a last-day 65.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies