Dempster carried a two-run lead into the fourth, courtesy of third-inning home runs by Mike Napoli and Ian Kinsler against Angels ace Jered Weaver.
After escaping a bases-loaded jam in the third, Dempster departed with two runs in and two runners aboard in the fourth. That's when things unraveled completely for Texas.
"It got out of control," Rangers manager Ron Washington said. "We couldn't get any outs. In that fourth inning, they just took the game from us."
Tanner Scheppers, born and raised a short drive from the ballpark in Orange County, hit Erick Aybar with his first pitch to load the bases. Scheppers' first pitch to Torii Hunter got past Napoli to the backstop. Chris Iannetta rumbled in from third and made contact with Scheppers at the plate, causing him to land awkwardly on his right knee and collapse to the ground. He was still there when Mike Trout roared in from second, scoring when Napoli's toss home hit umpire Jim Wolf.
Scheppers left with what would be described as a bruised right knee, pending further evaluation. Mark Lowe came in, and this is what followed: a walk to Hunter; 35-foot roller by Kendrys Morales for an RBI single; line-drive RBI single by Howie Kendrick; line-drive sacrifice fly by Vernon Wells; RBI double by Alberto Callaspo.
Iannetta said he had no intention of hurting the young pitcher.
"I felt bad because I tried to avoid him," Iannetta said. "I knew I was going to be safe. I put my foot down beforehand. He was on half the plate, so I just put my foot down before that and kind of popped up. I didn't see the replay. It looked like he may have gone for the throw from Nap, or whatever happened. When I was coming up, I saw he was on top of me and then he fell off, and I felt terrible. I don't ever want to see anyone get hurt."
The eight-run outburst -- handing Weaver a six-run lead en route to an 18-win season and 100th career victory -- finally ended when Mark Trumbo made his second out of the inning.
"Other than that [inning]," Dempster said, "we played a good baseball game."
And right up to its sinking, the Titanic was a nice ride.
Dempster had spotted the Angels a lead in the first. Aybar singled, stole second and scored when Hunter (6-for-6 in his career against Dempster) singled to center.
In two starts against the Angels since his arrival from the Cubs, Dempster has coughed up 13 runs on 15 hits in eight innings.
"I was actually missing down more than up," Dempster said. "That's a rarity."
This brief outing ended a run of five consecutive winning efforts by Dempster.
The Angels were without Albert Pujols, who stayed behind in Kansas City after his wife gave birth on Sunday morning to a daughter.
The Rangers had Josh Hamilton in the lineup. But he departed after his second at-bat in the third inning.
"We'll wait and see how he is [Wednesday]," Washington said. "He was having vision trouble with a sinus infection."
Returning to the lineup for the third time after missing 33 games with a quad injury, Napoli unloaded a tremendous homer to center leading off the third. It was his 19th of the season and his ninth in 16 games in his old home park, where he's hitting .424 since joining the Rangers in 2011.
"That was a Harmon Killebrew home run," Washington said. "He got it up in the air and it just kept carrying. He really crushed that one.
"Nap really enjoys playing here. It energizes him. I'm happy to see him swinging like that. Since he's come off rehab, he's been having much better at-bats. The time off help him mentally. He was struggling with some things, and the time off refreshed him."
Kinsler's homer following a Mitch Moreland single was his 18th of the season. Kinsler's drive into the left-field corner sent Wells tumbling into the first row of seats.
Weaver wasn't dominant, but he was good enough. He's 9-0 against the Rangers at Angel Stadium and is 12-7 overall against Texas in 29 career starts.
"He's a great pitcher, one of the best in the league," Michael Young said. "When he gets a lead, he knows what to do with it."
After the Angels added a run in the fifth against Yoshinori Tateyama on Aybar's third hit, 21-year-old right-hander Wilmer Font made his Major League debut for Texas. The 6-foot-4 Venezuelan set the Angels down, walking one hitter.
"He pounded the strike zone and looked good," Washington said. "That was a good debut."