Sixth seed Johnson won his third career ATP title, taking two in a row on Houston clay after his first victory came in 2016 at Nottingham.
Johnson, who is getting married next weekend, was the first back-to-back US Clay court winner since Andy Roddick in 2001-02.
American eighth seed Sandgren, who made a stunning run to the Australian Open quarter-finals in January, was playing in his first tour final.
Johnson, ranked five spots ahead of Sandgren at 51, had never before faced the shock Aussie Open upstart, who ousted Stan Wawrinka and Dominic Thiem, two top-10 foes, at Melbourne in January.
It was an emotional victory for Johnson, whose father Steve Sr. died 11 months ago and last saw him play in last year’s Houston final.
After the final point, Johnson made a cross sign and fist-pumped to the heavens, then buried his head on Sandgren’s shoulder, overcame by memories and the moment.
“I’m glad to have won again here in Houston,” Johnson said. “It means a lot.”
After Johnson dominated the first-set tie-breaker, Sandgren broke for a 4-2 edge in the second set and broke again in the eighth game to force a third set.
Johnson, 28, took the only break of the final set from Sandgren, 26, in the ninth game and denied the only break point he faced in the set in the close-out game.