He'll get that chance on Friday night against the AL Central-leading Royals, who open a season high-tying 10-game homestand.
Since surrendering four runs in his Royals debut - a 5-2 loss at the Chicago White Sox on April 3 - Santana (2-1, 2.48 ERA) has given up just four runs in 23 innings. All of those were plated in the first inning of his three starts.
"Once he gets settled in, he gets on a nice roll,'' manager Ned Yost said after Santana threw seven innings of two-run ball in Sunday's 4-2 win at Boston.
The former Los Angeles Angel has walked just five - none on Sunday - while striking out 26.
"When I don't give any walks, it gives me more opportunity to attack the zone and work more comfortably," Santana told the Royals' official website.
Kazmir (0-0, 16.20) admitted he was "a little jittery" in a 19-6 win at Houston on Saturday when he gave up six runs and eight hits over 3 1-3 innings. It was his first appearance since April 3, 2011, at Kansas City, where he gave up five runs in 1 2-3 innings of a 12-9, 13-inning defeat. The left-hander was put on the disabled list (lower back tightness) less than a week after that outing - his only one of 2011 - then was released two months later.
Kazmir spent last season pitching in the Atlantic League, and his 2013 season debut was pushed back due to an oblique injury.
"Overall, stuff I can take out of this start and bring into my next start is what not to do, I guess," he said.
Indians first baseman Mark Reynolds needs to maintain his approach at the plate. He's hitting .375 (6 for 16) with two homers and a team-best six RBIs on the first five games of the trip.
"Typically, Mark, when he's started out well, those have been his bigger years," manager Terry Francona told the MLB official website of Reynolds, who leads the club with seven homers and 19 RBIs.
Left fielder Alex Gordon could be on his way to one with the Royals (11-8). His batting average has been well above .300 since the first week of the season, and now he's starting to deliver some power, hitting both of his home runs during the last three games.
Gordon's first career grand slam was the big blow in the 10th inning as Kansas City capped off a 4-3 trip with an 8-3 win over Detroit on Thursday.
"I was just trying to make contact," he said.
Gordon hit .333 with three homers - tied with Billy Butler and Eric Hosmer for the team lead - and 11 RBIs off Indians pitching last season. Kansas City won 10 of 18 in this divisional matchup in 2012, including five of nine at Kauffman Stadium.
Cleveland (8-11) ended a five-game skid at Kansas City - and a seven-game slide in the series - with a 15-4 victory in its last game visiting the Royals on Sept. 23.
Santana dropped two of his three starts against the Indians last year to fall to 2-8 with a 4.71 ERA in 14 starts against Cleveland. However, one of those victories was a no-hitter on July 27, 2011, at Progressive Field.