Still, the Angels barely held off the Kansas City Royals, who own the worst record in the major leagues, for a 4-3 victory Monday night.
"It's very important. We have to play like we're playing against the Yankees, or against Boston," Santana said.
The right-hander gave up three runs and six hits in 6 2/3 innings. Rodriguez struck out three of four batters in the ninth.
"They were down 4-0 and came back. Even though they're not playing very well, they kept on playing," Rodriguez said.
The Royals fell to 16-46 as the two-time defending AL West champion Angels, in last place in the division with a 28-35 record, ended a three-game skid.
Dallas McPherson had three hits and drove in two runs to lead the Los Angeles offense.
Kansas City manager Buddy Bell was impressed by Santana, who walked one and struck out four.
"The kid's got good stuff, obviously, but he's got better command than you'd think he does, especially for a young power pitcher," Bell said. "I thought his command was probably the thing that made him most effective."
Held hitless by Santana (6-3) until the fifth inning, the Royals pulled to 4-3 in the seventh on Matt Stairs' two-run homer, his sixth, and a run-scoring single by Angel Berroa that chased the Angels' starter.
Bobby Keppel (0-2) gave up four runs and eight hits in 5 1/3 innings during his third major league start. The Royals' right-hander walked three and struck out one.
"Their young pitcher showed some moxie," Angels manager Mike Scioscia said. "He made some big pitches, struck out [Vladimir Guerrero] to end the fourth inning with men in scoring position. He kept them in the game."
Said Keppel: "The last two innings I kind of got into a rhythm and threw some good pitches down in the zone."
McPherson, who went 3-for-3, is 13-for-32 in his last 12 games after slumping for much of the year. He staked Los Angeles to a 1-0 lead with an RBI single in the second.
Stairs got the Royals' first hit when he singled sharply to right field leading off the fifth. Teahen singled with two outs, advancing Stairs to third, but Santana got John Buck on a fly ball to end the threat.
The right-hander allowed only one baserunner through the first four innings, a first-inning walk to Doug Mientkiewicz.
Center fielder Darin Erstad, activated earlier in the day from the disabled list, went 0-for-2 and walked twice for the Angels. He had been sidelined by irritation in his right ankle and was on the DL since May 1.
Angels RHP Bartolo Colon threw seven innings for Triple-A Salt Lake in his third minor league rehabilitation start, giving up six earned runs and nine hits against Fresno. The 2005 AL Cy Young Award winner has been on the DL since April 19 with inflammation in his right shoulder. ... Cabrera extended his club record by reaching base safely in his 42nd consecutive game. That's double his previous high of 21 in a row. Chili Davis had held the Angels' record of 36 games in 1995. ... Kansas City will send out its 12th starter of the season in the second game of the series when Brandon Duckworth (0-0) opposes rookie Jered Weaver (3-0). Duckworth, who has a 16-21 career record and a 5.34 ERA in 91 major league appearances, was acquired from the Pirates on Saturday for cash. Royals starters are 7-33.