CLEVELAND – The last-place Indians entered the series finale against Kansas City on Sunday with the opportunity to complete a sweep that would have gained three games on the fourth-place Royals.

They’re going to have to settle for one.

Despite a positive outing from Fausto Carmona, the Indians fell 6-2, failing to muster a win that would have pulled them even with Kansas City in the Central Division standings. Instead, they trail the Royals by two games.

Carmona (11-13, 4.19 ERA) pitched well enough to win, allowing three runs on six hits over 6 2/3 innings, but his personal losing skid was extended to five games with his sixth loss in seven starts.

“Fausto deserves a lot of credit,” said Cleveland manager Manny Acta, whose team lost for the first time in four games. “It’s a team game and he did his part. He gave us a chance to win. We couldn’t put anything together offensively against (Royals starter Bruce) Chen.

“We won the series, so that’s positive.”

A day after beating Royals ace Zack Greinke, the Indians struggled against the journeyman Chen, who allowed two runs on six hits over six innings, and shut Cleveland out on four hits over the first five.

Chen’s only blemish came on a two-run home run in the sixth inning from Jason Donald, who entered the game when Indians first baseman Matt LaPorta left with a left hip injury after batting in the fourth.

“He’s a crafty lefty,” Donald said of Chen, who entered the game with an 8-7 record and 4.88 ERA. “He’s a guy that mixes his speeds real well. He’s a veteran guy who knows what he’s doing on the mound.”

Carmona did too, with a new grip on his change-up continuing to pay dividends for the right-hander, but not enough to offset another sub par effort from Cleveland’s offense.

“He had a really good change-up with that new grip,” Acta said. “We were very encouraged by that.”

Carmona didn’t allow a run over the first three innings, but permitted the first three Royals to reach base in the fourth on a walk and two singles, which led to a pair of runs in the inning on consecutive sacrifice flies from Brayan Pena and Mitch Maier.

After Donald’s homer tied the game at two, Carmona surrendered a two-out RBI double to Kia Ka’aihue in the seventh that put KC in front for good, while saddling him with the loss.

Cleveland’s bullpen derailed a comeback notion by allowing three runs over the final two innings.

Left-hander Tony Sipp allowed a solo homer to Mitch Maier in the eighth, with Hector Ambriz surrendering two in the ninth, one on an error from shortstop Asdrubal Cabrera and another on a two-out single from Pena.

While the Indians bullpen showed some holes, Kansas City’s was iron-tight.

A trio of relievers combined to shut out the Indians on one hit over the final three innings.

Cleveland’s last seven outs were via strikeouts with KC’s Blake Wood and closer Joakim Soria fanning the side in the eighth and ninth innings.

Contact Chris Assenheimer at 329-7136 or cassenheimer@chroniclet.com.