An eighth-inning throwing error by Twins first baseman Logan Morrison on Segura's sacrifice bunt allowed Gordon to score the decisive run.
Four Seattle pitchers combined on a four-hitter to send Minnesota to its second straight setback.
Gordon led off the eighth inning with a double off Twins right-hander Trevor Hildenberger (1-1).
Segura laid down the bunt, and when Morrison fielded it, he looked briefly at third before turning and throwing toward first.
But the toss to second baseman Brian Dozier covering first went down the right-field line, allowing Gordon to score easily.
Nick Vincent protected the lead with a flawless eighth and fellow right-hander Edwin Diaz struck out the side in a perfect ninth for his American League-best 14th save.
The contest started one hour, 42 minutes late due to rain. The game was a makeup from a postponement on April 8.
Seattle was playing its first game without star second baseman Robinson Cano, who broke his right hand in Sunday's game against the Detroit Tigers. Cano was officially placed on the 10-day disabled list on Monday and is expected to miss six to eight weeks.
Mariners left-hander Wade LeBlanc tossed six scoreless frames. LeBlanc gave up three hits, struck out four and didn't issue a walk.
Lefty reliever James Pazos (1-0) got the victory after working out of a seventh-inning jam by stranding a runner at third.
Mitch Garver laced a one-out double to center and moved to third on Morrison's groundout before Pazos retired Eddie Rosario on a popup to second.
Minnesota right-hander Jake Odorizzi allowed four hits over six shutout innings. He struck out seven and walked one.
Seattle had runners on first and second in the sixth inning when Kyle Seager lined a bullet up the middle. But the ball caromed off Odorizzi's backside over to shortstop Ehire Adrianza, who stepped on second for a forceout.
Odorizzi then struck out Ryon Healy on his 97th and final pitch of the night to end the threat.
The Mariners were 1 for 13 with runners in scoring position. Minnesota was 0 for 2.
--Field Level Media
Seattle | Minnesota | |
Wade LeBlanc | Player | Jake Odorizzi |
No Decision | W/L | No Decision |
6.0 | IP | 6.0 |
4 | Strikeouts | 7 |
3 | Hits | 4 |
0.00 | ERA | 0.00 |
Seattle | Minnesota | |
Jean Segura | Player | Ehire Adrianza |
2 | Hits | 1 |
0 | RBI | 0 |
0 | HR | 0 |
3 | TB | 1 |
.667 | Avg | .333 |