"Each game with these guys is important," Weaver said. "Six back is not where we want to be. It's not what we're about.
"They've got a great club. If you make mistakes, you're going to pay for it."
Weaver was good, but Lee, moving to 9-4 for the season and 1-1 for Texas, was a tad better.
"It's an opportunity to extend our lead against those guys," Lee said. "They're right behind us. And any time you're playing anyone in the division, it's important."
Weaver was Lee's equal into the sixth, tied at 1, when Vladimir Guerrero hit a ground ball through the right side that became a hustle double when the angelic Ranger beat Bobby Abreu's throw from right-center.
"It was probably three to four inches outside," Weaver said of the pitch. "He turned what I thought was a single into a double."
Josh Hamilton followed with a drive to left-center for a double, cashing in Guerrero. Center fielder Torii Hunter, shading toward right-center, gave chase but couldn't get there.
"He popped a changeup up," Weaver said, clearly not happy with the outcome.
After an infield hit by Nelson Cruz, Bengie Molina, another former Angel, lifted a sacrifice fly to center, scoring Hamilton.
That run looked even bigger when Mike Napoli led off the seventh with a drive into the left-field seats, his 18th homer of the season and fourth in the past five games.
"I was trying to stay up the middle," Napoli said, "and he ran a cutter in."
Reaching the seats was the only sure way to avoid a Rangers glove. The Texas defense certainly didn't rest.
"We catch a break here or there," Napoli said, "and we're on top."
Neftali Feliz came on for the last two outs, pumping premium gas against Hunter (liner at Cruz in right) and Napoli (fly ball to center) to nail down his 26th save.
Texas' 56-40 record matches its best after 96 games, equaling the 1999 edition, and its six-game lead is its largest margin since that same season when it won the division by eight.
The Rangers are enriched by the acquisition of Lee from Seattle, and pairing him with Molina, a catcher who knows his stuff, courtesy of San Francisco.
"He definitely was in the strike zone early," Angels manager Mike Scioscia said of Lee. "He got back in counts with good pitches, not just strikes.
"They have a terrific defensive club with a lot of range -- definitely in the outfield they do. They don't depend as much on shrinking the field as some clubs because of their athleticism. They have a good defensive club with great range, and it showed tonight."
Lee's new gloved friends ran down a half-dozen bullets. Abreu hit three shots that could have been hits, Hunter a pair. Howard Kendrick drove right fielder Cruz against the wall in right to flag down his drive in the fourth inning.
"Defense wins games and championships," Hunter, the nine-time Rawlings Gold Glover, said. "Their defense was great tonight.
"Taking nothing away from Lee -- he pitched a great game -- but we hit the ball hard and had nothing to show for it."
Michael Young's opposite-field homer with one out in the first, his 13th of the season, gave Lee the lead.
"A fastball," Weaver said, "and he went with it."
Lee, resourceful and confident, maintained a quick tempo and protected the lead Young provided until doubles by Hideki Matsui and Maicer Izturis got the Angels even in the fifth.
Matsui drove the ball off the wall in center, beyond the reach of Julio Borbon, and Izturis lashed one to left-center that Hamilton managed to get a glove on but was unable to flag it down.
"Took a great athlete to get there," an admiring Hunter said of Hamilton.
Izturis has four RBIs in two games since spending five weeks on the disabled list with a strained left forearm.
Regaining control after Napoli's blast, Lee extended to seven his streak of consecutive games lasting at least eight innings with a spotless eighth. It is the longest such streak since Toronto's Pat Hentgen had a run of 12 straight in 1996, his Cy Young Award season.
"He throws strikes," Napoli said of Lee. "The last thing you want to do is be 0-2 [in the count]. He's sneaky. He commands both sides of the plate. And that cutter keeps you honest."
Weaver slipped to 9-6, giving up three runs on seven hits and two walks while striking out five. It was his third loss in his past four starts.
"I was trying to keep us in the game as much as possible," Weaver said. "I wish I could have gotten deeper in the game. Any time you hold that team to three runs in this park, you feel like you've done your job."
Before the game, the Angels acquired Royals infielder Alberto Callaspo, who is expected to join the team for Friday night's game matching C.J. Wilson against Joe Saunders in a duel of southpaws.