Haniger's infield grounder with the bases loaded brought home the winning run in the 11th inning to give the Mariners a 5-4 victory over the Rangers on Friday night.
Encarnacion hit a three-run homer and drove in all the other runs for the Mariners.
''Edwin had a big night at the plate,'' Mariners manager Scott Servais said. ''We didn't do a lot with the bat tonight but we put together that little rally and grinded through some at-bats. Everybody chipped in on this one.''
Omar Narvaez singled with one out in the 11th before Ryon Healy and Dee Gordon walked to load the bases off Kyle Dowdy (1-1). Haniger hit a grounder to third that was bobbled by Logan Forsythe as he threw to second base, hoping to start an inning ending double play. But it was too late to get Gordon and the ball was dropped by Rougned Odor.
''I just tried to break up a double play,'' Gordon said. ''I didn't know he bobbled it, but it helped us a little bit.''
Roenis Elias (2-0) pitched two scoreless innings to earn the win. The Mariners used eight pitchers on a night when they started with rookie Yusei Kikuchi as an opener.
The Mariners led 4-3 in the ninth inning before a pinch-hit home run by Shin-Soo Choo off reliever Anthony Swarzak tied the game.
Kikuchi, who made his sixth start of the season, had a two-strikeout, nine-pitch first inning before calling it a night. This is part of the plan for Kikuchi to limit his innings this season as he adjusts to the major leagues. Starting pitchers in Japan typically pitch only once a week.
Justus Sheffield, acquired by the Mariners in the trade that sent James Paxton to the Yankees, was recalled from Triple-A Tacoma to make his season debut in the second inning. He allowed two runs in three innings of relief while walking four and striking out three.
''I was just happy to get out there and try to keep the game close,'' Sheffield said. ''Guys were telling me just to catch my breath and settle down out there.''
Shelby Miller allowed four runs in five innings as the Rangers lost their fifth consecutive game. Rangers right fielder Nomar Mazara had three RBIs, including a two-run homer off Sheffield.
Shortstop Elvis Andrus played in his 1,500th game Friday since his Rangers debut on April 6, 2009. It makes him the fifth player to reach that milestone in a Rangers uniform.
HEARN ON IL DAY AFTER MLB DEBUT
Rangers LHP Taylor Hearn, who recorded only one out while facing eight batters in his major league debut Thursday, was placed on the 10-day IL Friday with tightness in his left elbow. Hearn will see a doctor back in Texas on Saturday, but team officials don't think the injury is serious.
RHP Wei-Chieh Huang was recalled from Double-A Frisco one day after being optioned for Hearn's debut.
Rangers: 2B Rougned Odor rejoined the team Friday and was activated off the IL after a two-game rehab assignment in Nashville. Odor was placed on IL April 11 with a right knee sprain. . RHP Ariel Jarado also was recalled from Nashville Friday. . LHP Jeffrey Springs and INF Jeffrey Wisdom were optioned to Nashville.
Mariners: RHP Shawn Armstrong was designated for assignment Friday when the team recalled Sheffield from Triple-A Tacoma.
Rangers: 3B Asdrubal Cabrera, who left Thursday's game in the second inning with tightness in his left calf, had an MRI Friday and it was negative. He took BP in the cage Friday, but did not play and is listed as day-to-day.
Mariners: Jay Bruce returned to the starting lineup, playing right field, after missing four consecutive games with tightness in his quad.
Rangers: LHP Mike Minor (2-2, 3.21) will make his sixth start of the season Saturday night in Seattle. Minor has allowed two earned runs or less in three of his last four starts, including a shutout on April 16. But he took the loss at Oakland on April 22, allowing four runs on four hits in six innings. Minor was 0-2 in four starts against Seattle last season, posting a 6.87 ERA in those games.
Mariners: RHP Mike Leake (2-2, 4.30) will make his sixth start of the season Saturday night against Texas. Leake is one of only three pitchers (with Jon Lester of the Cubs and Max Scherzer of the Nationals) to make at least 30 starts every season from 2012 through 2018.
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