The visiting Royals have had trouble hitting Jimenez this year but they have won eight straight outings by Shields heading into Sunday's matchup.
Jimenez (7-4, 4.37 ERA) is 1-0 with a 2.55 ERA in three starts against Kansas City (43-48), beginning with seven outstanding innings in a 9-0 road win April 29.
He failed to receive decisions in the next two, allowing two runs over 5 2-3 innings in a 4-3 victory June 18 and giving up four runs over five-plus frames in a 10-7 loss July 4.
Jimenez's walk total has increased from two to four to five in those starts, and he owns an AL-worst walks per nine innings ratio of 4.85.
The right-hander is limiting the Royals to a .131 average - the lowest among teams that have faced him this year. The only Kansas City hitters with more than one hit against him this season are Lorenzo Cain (3 for 8) and Mike Moustakas (2 for 8). The Royals have just three other hits off Jimenez.
Shields (4-6, 3.12) has not lost since May 27, going 2-0 with a 3.38 ERA in his last eight outings. He limited the Yankees to one run over seven innings Tuesday in a 3-1 victory, finishing with five hitless frames.
The right-hander has no record with a 4.76 ERA in two 2013 starts against the Indians - both during the Royals' eight-game run with him on the mound.
Nick Swisher did not play in those games, once due to injury. He's faced Shields more than any Indians hitter, going 8 for 45 with three homers.
Cleveland (50-44) will head into the All-Star break in second place in the AL Central for the second straight year, but probably feels better about itself now. Last year, the Indians trailed the second-place White Sox by three games before manager Manny Acta was fired near the end of a 24-53 collapse thereafter.
Under new skipper Terry Francona, the Indians are 1 1/2 games behind Detroit as they seek a fourth straight win Sunday.
"What we've done in the first half makes the second half potentially really exciting," he told the Indians' official website. "We've played well enough where, let's go play. That's exciting. We need to play better in the second half, but we can."
Lonnie Chisenhall came through with his first career grand slam in Saturday's 5-3 victory. He's hitting .292 with three homers and 14 RBIs since being recalled from Triple-A Columbus on June 18 after being sent down May 15.
"When he's getting balls to hit he's not fouling them," Francona said. "Sometimes you get one pitch to hit in an at-bat. Now he's getting it and hitting it."
Kansas City has totaled eight runs with 32 strikeouts and a .213 average during a four-game slide. Alex Gordon is in a 1-for-17 slump, Salvador Perez a 2-for-23 rut and Billy Butler a 6-for-39 skid although he had two hits Saturday.