After the Yankees' third error of the game allowed Jeremy Reed to reach third base, Olivo singled home the go-ahead run in the eighth inning as Seattle rallied for a 7-6 victory Wednesday night.
"We gave them too many outs," New York manager Joe Torre said. "It was not a pretty game."
The Yankees still had a chance for their first 11-game winning streak in nearly 20 years after loading the bases in the ninth, but Ron Villone struck out Jason Giambi on three pitches for the final out and his first save since 1999, when he pitched for Cincinnati.
Giambi extended his hitting streak to six games with a two-out, two-run single to right in the third inning that Seattle's Ichiro Suzuki couldn't make a shoestring catch on.
But Giambi couldn't come through in the ninth, taking a called third strike.
"I got caught looking slider and he threw a fastball," Giambi said. "He made some good pitches. He did his job."
Gordon got Greg Dobbs to pop out to third, but Olivo hit an 0-1 pitch into center field, scoring Reed. Olivo had been hitless since ending an 0-for-27 slump with three hits Sunday against Boston.
"I just stayed closed and made contact with the ball," said Olivo, who picked up his first hit in the series.
The Yankees led 6-4 with two outs in the sixth before making a pair of errors that allowed Seattle to tie it.
Reliever Tanyon Sturtze struck out Olivo, but the ball bounced and catcher Jorge Posada was unable to pick it up, allowing Olivo to reach first.
"His hustle certainly got us two runs," manager Mike Hargrove said. "I don't think you'll ever see Miguel Olivo not hustle. That's his nature."
"I don't think anything was simple today for us," Villone said.
Alex Rodriguez hit his major league-leading 14th home run, a three-run shot on a 3-1 pitch from Seattle starter Jamie Moyer that Rodriguez hit into the right field seats. Rodriguez leads the league with 41 RBI.
But New York failed to hold leads of 4-0 and 6-2. The Yankees were trying to sweep the Mariners for the second time in a week.
"It was very frustrating not to come away with a win," Rodriguez said. "The lesson is when you've got a team down, you got to put them away."
New York last won 11 straight from Aug. 31 to Sept. 10, 1985.
After taking two of three from Boston, Seattle had dropped its last two.
Mike Mussina pitched five innings, allowing four runs and seven hits with six strikeouts for New York, but lost out on his fourth straight win after Seattle scored twice in the sixth.
"He had good stuff, he just didn't have good command early," Torre said. "He left the game with a lead and we should have been able to hold it."
Moyer was pulled after the fifth, giving up six runs and eight hits. He allowed five runs in the first inning at Yankee Stadium a week ago and is 0-2 in his last four starts after starting 4-0.
Seattle scored twice in the first on an RBI double by Raul Ibanez and an RBI single by Bret Boone. The Mariners added two more in the fifth on a two-out, two-run double to left-center field by Ibanez, but Mussina got out of the jam by getting Richie Sexson to fly out.
"Our guys stayed on it, stayed with it tonight," Hargrove said. "The deeper the game went, we had better at-bats. It finally paid off."
Mussina started the Yankees' streak with a four-hit shutout of Oakland on May 7, and beat the A's again last Friday, allowing two runs and striking out a season-high nine.
Wednesday's start was his shortest outing since lasting five innings April 13 in an 8-1 loss at Boston.
- Mussina has the best winning percentage of any pitcher ever against Seattle (minimum 15 wins). He is 17-5 against the Mariners.
- Moyer has allowed 23 runs and 35 hits in his last four starts (15.15 ERA).
- Tony Parker and Robert Horry of the San Antonio Spurs were in the stands. The Spurs play the Seattle SuperSonics in Game 6 of the Western Conference semifinals Thursday night.
- University of Washington men's basketball coach Lorenzo Romar threw out the first pitch.