Fowler, 29, has now notched eight top-five finishes or better in the majors from 33 appearances.
The four-time PGA Tour winner birdied six of the last 11 holes at Augusta National on Sunday including a clutch birdie putt from seven feet at the last to heap pressure on Reed in the group behind, but it was of small consolation as Reed went on to make par up 18.
Fowler has come under fire for his lack of form over the weekends in the big tournaments, but he answered a few critics at Augusta when shooting rounds of 65 and 67, with 11 birdies, an eagle and one bogey.
“I'm ready to go,” he added. “I'm really looking forward to this year and the three majors that are left.”