Seager had no chance even if he'd gloved the ball, as Springer's chop had too much hang time for a drawn-in infield to make a play at the plate with no outs and the bases loaded.
Mariners manager Lloyd McClendon said Seager only would have had a chance if he'd gotten a ball hit waist-high, right at him.
"There's not a lot you can do about that," McClendon said. "That's the way it goes. That's baseball."
Altuve led off the 11th with a single up the middle, and Dexter Fowler dropped a perfect bunt down the first-base line to put runners on first and second. Carlos Corporan then dropped a bunt that Furbush fielded but was late with the throw trying to get Altuve at third, loading the bases to set up Springer.
"It was a great bunt, so I tried to make the best play I could and didn't get it done," said Furbush (0-3).
That set up the recently promoted Springer, a highly touted prospect who is hitting .180 while trying to fill the Astros cleanup role. But Springer came through with Houston's first walk-off win of the season as they improved to 10-19.
"I hit and I saw it and I said, 'Please get over his head,'" said Springer. "I guess I hit it just high enough to get off his glove."
The Mariners have had their struggles with the last-place Astros, losing for the third time in four meetings this season. Seattle is 11-12 against the Astros since they joined the AL West last year.
The Mariners rode a hot streak into the series opener, having won five of six after snapping an eight-game losing streak. But the extra-inning setback drops them to 12-15 for the year and 2-1 on their current nine-game road trip after taking two games in New York.
But with Felix Hernandez battling a stomach flu that left him feeling lethargic, the Mariners got only five innings from their ace right-hander as he gave up three runs (two earned) on five hits, three walks and a hit batter.
"Felix was under the weather," McClendon said. "He didn't have much strength going out there. He battled and gave us five innings. I didn't know what we'd get out of him. I knew he was drained. He was sick yesterday and very weak today. He did a great job for us and kept us in the ballgame."
Hernandez struck out six, threw 89 pitches and was still in position to win until Houston tied the game with a run off reliever Yoervis Medina in the eighth.
The Mariners' ace hasn't been sharp in his last three outings after a sensational start this year, but the no-decision leaves his record at 3-1 with a 2.53 ERA.
This one, he said, was much different however, as he lost nine pounds over the past two days and was still sweating as he talked to reporters after the game.
How much did the illness affect him?
"A lot," Hernandez said. "But I still have to go out there and do my job. That's the reason I'm here. I tried not to waste a lot of energy. I just tried to go out and make good pitches and be economic, but they were fouling off a lot of pitches. I wasn't throwing a lot of strikes."
Mike Zunino cracked a two-run home run to tie the game, 2-2, in the fifth inning, and Seager delivered a two-run, bases-loaded double in the sixth to give Seattle a 4-3 lead before Hernandez's departure.
Seager has racked up 13 RBIs in the last nine games to move into a share of the team lead with Justin Smoak with 15 on the season.
After Seager's double put runners on second and third, Astros starter Brad Peacock limited damage by striking out Smoak and getting Dustin Ackley to ground out.
Hernandez struggled with his control early, but worked out of trouble until the Astros took advantage of some shaky defense for two runs in the third inning.
After Altuve led off with a bunt single, Fowler hit a hard shot that shortstop Brad Miller couldn't handle. Fowler was given a single, and Jason Castro followed with high fly that Abraham Almonte simply missed as he drifted back near the base of Tal's Hill in center field.
Almonte was given an error, leading to an unearned run. Almonte committed another error in the sixth inning, though that one didn't result in any damage.