But a blown save opportunity in the ninth inning crushed all hope of a series-salvaging victory in Houston's 6-5 loss.
Will Harris allowed three earned runs in the top portion of the ninth, blowing a two-run lead for the Astros.
Two innings before that, the defending World Series champions finally plated a run Thursday afternoon, snapping a 28-inning scoreless streak dating back to the series-opening game on Monday.
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Masahiro Tanaka continued the Yankees' dominance of the Astros order in six innings of work, allowing five hits. But the seventh inning offensive explosion culminated in to two bases-loaded situations, forcing manager Aaron Boone to pull his starter.
Chad Green then allowed back-to-back RBIs and an Alex Bregman run off of a wild pitch, giving the Astros the tie at 3-3.
George Springer followed in the next at-bat with a hit to the mound on a sacrifice grounder to send Marwin Gonzalez home. The Astros took the lead, 4-3.
Carlos Correa, who added to his unbelievable fielding mixtape with a difficult catch and throw to first in the top seventh inning, launched a rocket of a homer to the train tracks in left for the 5-3 lead in the eighth.
Houston's starter Lance McCullers Jr. was dinged early for three earned runs, including two in the second inning.
The Astros' late game offense was a reversal of the team's fortune in the middle two games of the series. Houston lost back-to-back games in which the Astros were shut out.
Houston falls to 20-13 heading into six consecutive days on the road. The Astros have a three-game interleague series with the Arizona Diamondbacks starting Friday. The 'Stros then head to Oakland for a three-game series with the Athletics beginning Monday.