Texas took three of four in the series, scoring 35 runs in the process. The Tigers have lost six of seven, and even Verlander (5-4) couldn't come close to stopping the slide.
The Detroit right-hander allowed nine runs - six earned - in 5 1-3 innings in one of the worst starts of his career.
Michael Choice homered for the Rangers in the second, and Texas broke the game open with five runs in the fifth.
Colby Lewis (4-3) allowed two runs and five hits in 5 2-3 innings.
Detroit slugger Miguel Cabrera left the game in the seventh with a right hamstring cramp.
Verlander has allowed 16 earned runs in his past three starts, and although the Tigers still have the best record in the American League, they have to wonder when this alarming stretch of poor pitching will end.
Other starters have struggled too. In its past seven games, Detroit has allowed 57 runs.
The nine runs allowed by Verlander equaled a career worst, and he allowed 11 hits. Verlander finished with only one strikeout, his fewest in a regular-season game since May 31, 2008, when he also struck out one at Seattle.
Even without injured slugger Prince Fielder, the Rangers romped through Motown, scoring at least nine runs in all three of their victories in this series.
Choice broke a 1-all tie with a second-inning homer off Verlander, and after a double by Chirinos, Rougned Odor dropped a bunt that Verlander threw away for an error, allowing a run to score.
Texas led 3-2 in the fifth when Shin-Soo Choo led off with a walk and went to third when Elvis Andrus' grounder went past shortstop Andrew Romine for another Detroit error. Moreland and Beltre followed with consecutive RBI singles, and a two-run triple by Rios made it 7-2.
Chirinos singled home Rios two outs later.
The Rangers tacked on three runs in the seventh to make it 12-2 on RBI singles by Andrus, Moreland and Beltre. Cabrera came out of the game after singling in the bottom of that inning, and to make matters worse for Detroit, reliever Joba Chamberlain left in the eighth with a right ankle contusion.
The Rangers finished with 17 hits, bringing their total for the last two games of the series to 36 - with 14 for extra bases.
NOTES: Even Sunday's time of game was the same as the day before: 3 hours, 43 minutes. ... Choo, who left Saturday's game with a sore left ankle, was back in the Texas lineup a day later but as the designated hitter. ... Detroit 2B Ian Kinsler extended his hitting streak to 11 games. ... The Tigers head to Oakland for a four-game series between the teams with the two best records in the AL. Detroit LHP Drew Smyly (2-2) faces Oakland LHP Tommy Milone (2-3) on Monday. ... Texas heads to Minnesota, with RHP Nick Tepesch (1-0) taking the mound Monday against Twins RHP Kevin Correia (2-5).