Rodriguez, whose season debut was delayed after offseason knee surgery, has followed a 3 2/3-inning debut on April 8 with a career record-tying three-game run of quality starts, all resulting in wins.
He has worked 18 2/3 innings, yielded six earned runs and struck out 16 during that span and will face veteran right-hander Jason Hammel in the series opener.
On Sunday, the Red Sox got "help" from suspended reliever Joe Kelly, who left his comfortable seats and went out to the bleachers behind the bullpen with his team down 3-0. They rallied to tie and then won when Sandy Leon poked a single past third base in the eighth inning.
"I got suite tickets from (club president) Sam (Kennedy)," Kelly said. "Sam lets me come up there. We had no runs so gotta get out of the suite and be able to switch it up."
He didn't stay long, but it worked.
Despite four losses in their last seven games, the Red Sox are 20-7, matching the second-best start in franchise history. The 1946 team opened 23-4 (and went to the World Series). They were 20-7 in both 1994 and 2002.
Boston faces a Kansas City team that has won two in a row for the first time this season but still comes in at 7-20.
The Red Sox's 18 April wins have tied a franchise record as they head into Monday night's April finale.
Boston is also only the fifth team since 1913 with at least 20 victories by May 1. The 2014 Milwaukee Brewers were the last team to do it (remember, the schedule used to start later in April).
The Royals made their seventh attempt at a two-game winning streak at home against the Chicago White Sox on Sunday -- and this time it happened with a run in the eighth inning.
Whit Merrifield, who had been 1-for-18 with runners in scoring position, drove in the winner and Cheslor Cuthbert hit his first two homers of the season.
With closer Kelvin Herrera not available, former Red Sox right-hander Blaine Boyer posted his first save since 2016.
Rodriguez is 1-1 with a 4.98 ERA in four career starts against the Royals, whose current roster is hitting a combined .311 (14-for-45) against him. Merrifield is 3-for-3 and Alex Gordon 3-for-6, but Alcides Escobar is 1-for-6 (.167) and Salvatore Perez 1-for-7 (.143) off the left-hander.
Escobar left Sunday's game with a bruised left hand after getting hit by a pitch (and then scoring the winning run before leaving for the ninth inning) and is considered day to day. However, Yost said, "Jason Vargas called him, 'The Shark.' He's got no bones, just cartilage. He heals really, really quick."
Hammel is 3-3 with a 4.25 ERA against Boston in 15 games and eight starts -- 2-1 with a 4.45 ERA in ERA in nine games and four starts, at Fenway Park. Hanley Ramirez has worn him out to the tune of 9-for-19 (.472) with a home run. Mitch Moreland is 3-for-7 (.429) and Xander Bogaerts 2-for 6 (.333).
Cuthbert hit his first homer since Aug. 20, a span of 109 at-bats.