Bryant, who wound up at 16-under 272, earned his second win on the PGA Tour. His other was at the 2004 Texas Open.
Couples had a final-round 69 to finish second at 273.
Tiger Woods, a three-time Memorial winner, also had a 68 and tied for third at 12-under 276. Woods was tied by Bo Van Pelt and Jeff Sluman, who held at least a share of the lead after each of the first three rounds.
Bryant, 42, was one of four co-leaders leaders entering the final round.
"I feel really good. I'm very blessed to win here, my second win," said Bryant, who earned $990,000.
With the tie for third, Woods will remain No. 2 in the world behind Vijay Singh, who missed the cut here. If Woods had finished alone in third, he would have overtaken the Fijian.