Palmer, who is angling to make the postseason roster as a long reliever, made a strong case as he allowed just three baserunners while improving to 11-2 in his rookie season.
"It was quite comfortable," said Palmer, who replaced scheduled starter Jered Weaver in the rotation on Wednesday. "I felt good with what I was doing and I didn't feel like I had any pressure on me so went out there and threw the ball well."
Palmer, despite his impressive outing, remained humble after the game.
"I don't expect to be anywhere, but I've felt that I've done a great job this year and that I'll continuing doing a great job so that I'll be on the playoff roster," Palmer said. "That's for sure. I think I can help the team."
Palmer, though, wasn't the only Angels pitcher to have an impressive night. Darren Oliver, Jose Arredondo, Kevin Jepsen and Rafael Rodriguez each threw a hitless inning for the Angels.
The team's combined one-hitter was the Angels' first since July 27, 2004, against the Rangers and just the fourth time it's been done in franchise history.
But as for the game ball, Palmer wasn't sure who had it.
"I didn't get it," Palmer said with a laugh. "I don't have the ball. It's not me."
Meanwhile, the Angels' offense did more than enough against the Rangers and tied a franchise record (set in 1979) with their 866th run of the season.
"It says a lot," catcher Mike Napoli said of the tying the record that's sure to be broken with four games remaining this year. "We all worked together and clicked together this year, and it just happened. I don't know what to put on it but we're just doing our thing."
The Angels offense got to left-hander Derek Holland by scoring two runs in the fourth and another in the fifth before adding one more in the seventh.
Torii Hunter and Juan Rivera had RBI singles in the fourth, while Chone Figgins plated a run in the fifth on a single to score Maicer Izturis from second base. Gary Matthews Jr. later connected for a ground-rule double in the seventh to score the Angels' fourth run of the game.
Matthews' double also knocked Rangers starter Derek Holland out of the game after allowing four runs on eight hits over 6 1/3 innings.
The Angels then added their fifth and final run in the eighth inning on an RBI single by Terry Evans to score fellow reserve Brandon Wood.
The Angels began the night with Bobby Abreu as the only regular not in the lineup, but the Angels made mass substitutions later in the game so that first baseman Kendry Morales and outfielder Gary Matthews Jr. were the only players to play nine innings.
Scioscia compared the game to a Spring Training game in that regard but said that his team has maintained its intensity despite clinching the division with their win over the Rangers on Monday.
"These guys haven't let up one bit," Scioscia said. "Even now they're playing hard and understand they need to keep their edge. And even the kids are playing well, too."