New York took a 2-1 advantage in the best-of-five AL Division Series and can eliminate the Orioles in Game 4 on Thursday.
The left-handed hitting Ibanez came on as a pinch-hitter for Alex Rodriguez with one out in the bottom of the ninth and the Yankees trailing 2-1.
He launched a 1-0 pitch from Jim Johnson 10 rows deep into the right field seats to tie the game and give Johnson his second blown save of the series. Johnson led the majors in saves this season, but has given up six runs in his three appearances against the Yankees this week.
Ibanez came up again to lead off the 12th against Brian Matusz and hit the first pitch he saw into the second deck in right. Ibanez hit 19 home runs during the regular season, only the second time in the last eight years he had failed to reach 20.
His heroics spoiled a tremendous start for Baltimore's Miguel Gonzalez, who allowed a lone run through seven innings on five hits without a walk and with eight strikeouts.
Darren O'Day worked a perfect eighth for the Orioles, but Johnson let it get away in the ninth.
Baltimore's runs came on homers by Ryan Flaherty in the third inning and Manny Machado in the fifth. Both those shots were hit off starter Hiroki Kuroda.
Kuroda worked into the ninth inning and gave up only five hits. He received a standing ovation when he left the mound with one away in the ninth.
Jeter found a ball off his left foot early in the contest and limped throughout the contest before being replaced in the late innings.
The victory went to David Robertson, who did not give up a hit while working both the 11th and 12th innings.
Chris Tillman will start in a must-win situation on Thursday for Baltimore. The Yankees will go with Phil Hughes.