These Royals are nothing if not resilient.

One day after a crushing loss in the series opener the Royals rebounded Tuesday with a 6-3 victory over the Cleveland Indians that once again resuscitated their postseason hopes.

Alcides Escobar hit his first homer since April 28 and delivered another key RBI single that blunted a Cleveland comeback. Jeremy Guthrie rode strong defense through six effective innings.

And Luke Hochevar struck out five straight batters in a magnificent outing that picked up an ineffective Kelvin Herrera before Greg Holland closed out the victory for his 41st save.

The victory came one night after the Royals squandered a ninth-inning opportunity in a 4-3 loss and it snapped a six-game losing streak at Progressive Field.

It also pulled the Royals 76-69 to within three games of Tampa Bay in the battle for the American League’s final wild-card berth. Three other clubs — Baltimore Cleveland and New York — are between the Royals and Rays.

Guthrie 14-10 yielded one run in the first inning but nothing further in a 99-pitch outing before handing a 5-1 lead to Herrera to start the seventh inning.

Guthrie allowed nine hits but benefited from three double plays while striking out two and walking none.

Herrera ran into quick trouble when singles by Yan Gomes and Lonnie Chisenhall put runners at first and third with one out. Herrera was checked twice for apparent blister problems on his hand but remained in the game.

And he then surrendered a two-run double to Michael Bourn when left fielder Alex Gordon missed on a diving attempt in the gap that cut the lead to 5-3.

In came Hochevar who struck out Nick Swisher and Jason Kipnis.

The Royals got one run back in the eighth after David Lough pulled a one-out triple past first into the right-field corner. Escobar followed by driving an RBI single through the left side of a shortened infield.

Hochevar then struck out the side in the eighth which got the game to Holland.

It was 1-1 when Eric Hosmer opened the sixth inning with a walk against Cleveland starter Zach McAllister. A double by Billy Butler into the left-field corner moved Hosmer to third with no outs.

Mike Moustakas then broke a zero-for-16 skid (since his walk-off homer last Thursday’s victory over Seattle) with a two-run double into the right-field corner.

When Salvy Perez followed with an RBI single into center the Royals had a 4-1 lead and the Indians went to their bullpen for Nick Hagadone who retired the next three hitters.