Vance Worley struggled through 5 1-3 innings, but a strong performance by Minnesota's bullpen enabled him to earn his first win in 13 starts dating to Aug. 1, 2012.
Matt Wieters connected for the Orioles, who lost for just the second time in seven games.
Up 6-5 in the sixth, Doumit hit his third home run of the season, a two-run shot into the second deck in left field to give Minnesota a little breathing room at 8-5.
Brian Duensing pitched two innings of scoreless relief, Casey Fien got two outs and Jared Burton earned his first save in two chances with a perfect ninth.
It was a far cry from Friday night when the Twins' bullpen gave up six runs as Baltimore rallied from a 6-0 deficit to win 9-6 in 10 innings.
Worley (1-4) gave up 11 hits and five earned runs. He struck out one but threw 111 pitches.
He was hit hard in the first inning when Baltimore took a 3-0 lead. Manny Machado and Adam Jones had doubles, and Markakis and Chris Davis had RBI singles in the frame. Wieters added a sacrifice fly to deep left-center.
Worley got out a bases-loaded jam in the fifth and allowed one run in the sixth before Duensing came in and got Markakis to hit into an inning-ending double play.
Making his season debut for the Orioles, starter Steve Johnson (0-1) cruised through the first two innings, before he began to get behind in counts and the Twins took advantage.
Trailing 4-2 and with two outs in the fourth, Brian Dozier laced a two-run double into the left-field corner to tie it. After an intentional walk to Mauer and a walk to Doumit, Morneau lined a two-run single over the shortstop for a 6-4 lead.
Johnson, who was 4-0 with a 2.11 ERA in 12 games (four starts) for Baltimore last season, hoped to make the Orioles as the team's fifth starter out of spring training, but strained his right lat muscle in late-March.
In four innings, he allowed seven hits and six earned runs while striking out three. However, he walked four batters and just 48 of his 88 pitches were strikes.
Trailing 3-0, Eduardo Escobar doubled leading off the bottom of the third and scored on a double by Mauer. It was the 600th career RBI for Mauer, who scored on Morneau's single.
Wieters homered in the fourth for a 4-2 Baltimore lead.
NOTES: Johnson is the ninth pitcher to start for Baltimore this season, tying the Orioles with the Los Angeles Dodgers for most in the majors. ... To make room for Johnson on the roster, Baltimore optioned RHP Alex Burnett to Triple-A Norfolk. ...