The American made six birdies to finish on 17-under-par, ahead of Harris English in second, while Ryan Palmer and Webb Simpson ended tied-third.
Victory in Texas was Spieth's first since his final day collapse at the Masters in Augusta last month.
"That is a tough hump to get over," said Spieth, 22. "To win in front of my home fans, what a great week."
"I was never going to come out and say it until I was able to get over it - but that was a really tough hurdle for me to get over.
"I wouldn't want anyone to go through what I went through on that back nine at the Masters, so to win on the third tournament back [was great]".
Leading by one shot overnight, Spieth levelled through the first nine, before making six birdies on the back nine to claim his eighth PGA Tour triumph and the first in his home state of Texas.
Spieth, who is from Dallas just 33 miles away from the course, is the youngest eight-time winner in 86 years since Horton Smith.
He is also the second youngest eight-time winner in PGA history.
"Victory means a lot and the crowds were fantastic. It was a really cool atmosphere to play for. I stayed patient and the birdies came in streaks."
The top three players in the world, Jason Day, Spieth and Rory McIlroy, go into the Memorial tournament on Thursday having won their last events.
World number two Jordan Spieth scored a final round 65 to win the Colonial National Invitational by three shots.