Ceddanne Rafaela celebrates after scoring on a single by Masataka Yoshida in the sixth inning of the Red Sox’s 6-5 win over the Royals on Tuesday in Kanas City, Mo. Reed Hoffman/Associated Press

KANSAS CITY, Mo. — Dominic Smith scored the go-ahead run on a wild pitch in the sixth inning on a call that was overturned on a challenge, and the Boston Red Sox beat the Kansas City Royals 6-5 on Tuesday night.

Smith doubled to open the sixth and moved to third on a single to center field by Eric Sogard. After David Hamilton struck out looking, Smith charged home on a pitch by KC’s Seth Lugo that bounced in front of the plate and got away from catcher Salvador Perez. Perez chased the ball to the backstop, wheeled and threw to Lugo, who appeared to tag Smith for an apparent out.

The Red Sox challenged the call, which was overturned on review.

Later in the inning, with the bases loaded and two out Yoshida singled through the right side, driving in two more runs.

The Red Sox, who have won the first two games of the three-game set, trail the Royals by a half-game for the third American League wild-card spot.

Brennan Bernadino (4-3) worked a third of an inning and earned the win in relief. Kenley Jansen picked up his 21st save.

Lugo (13-6) allowed six runs, four earned, on six hits in 5 1/3 innings in the loss.

Boston held a 6-3 lead heading into the bottom of the eighth inning when the Royals’ MJ Melendez lined a two-run double to the wall, scoring Vinnie Pasquantino and Perez and cutting the deficit to a run.

Kansas City’s Bobby Witt Jr. lined a one-out double in the first before Pasquantino pulled one through the right side of the infield for an RBI single.

The Red Sox answered with a pair of unearned runs in the second. Connor Wong singled. Smith hit a grounder to second, but Michael Massey failed to field it. With one out, David Hamilton bounced one over the wall, scoring Wong. Smith scored on a groundout by Ceddanne Rafaela.

Masataka Yoshida homered with one out in the third to extend the Boston lead to 3-1.

The Royals used three straight two-out hits to tie the game in the fifth. Massey launched a 434-foot home run to right center. Witt followed with a bloop single and scored on a double by Pasquantino.

TRAINING ROOM:

Red Sox: Boston Manager Alex Cora said RHP Chris Martin played catch Monday and felt good Tuesday, so it’s likely he’ll be activated from the injured list before Wednesday’s game. He has been on the IL since July 5 (retroactive to July 4) with right elbow inflammation. … OF Tyler O’Neill, who has been out of the lineup with an illness since Aug. 3, feels better and is also likely to return to the lineup Wednesday.