The AL Central-leading Tigers improved to 42-21 at home and have a relatively comfortable cushion over the Minnesota Twins and the Chicago White Sox.
"This is a different ballclub than 2006, but there's a lot of good karma and good guys just like we had," said Verlander (15-7), a rookie for the AL champions when they lost to the St. Louis Cardinals. "It's a very similar-type feeling and obviously, that was a fun year."
The Rays, meanwhile, are not enjoying their season after winning the AL pennant.
"We let it get away," manager Joe Maddon said. "We've done that too many times, and that's why our record is where it is."
Tampa Bay fell to 28-38 on the road and 11 games over .500 overall, heading home for a possibly pivotal series against the wild card-leading Boston Red Sox.
"We can't afford to lose games like the one we lost today," Rays outfielder Carl Crawford said. "We're getting close to the line where we are going to be eliminated."
Verlander surrendered three runs, six hits and four walks over eight innings and struck out four, matching a season low. Fernando Rodney pitched the ninth for his 29th save in 30 chances.
Niemann was replaced in the eighth with a 3-1 lead after Clete Thomas hit a leadoff double. After Balfour retired the first two batters he faced, Curtis Granderson walked and Polanco hit his eighth home run of the season, snapping an 0-for-13 slump.
"I had challenged the first two guys and I felt great, but when I pitched around Granderson, it put me on the defensive," Balfour said. "Polanco squared up a fastball, which is going to happen, but it happened at the worst possible time."
Niemann retired the Tigers in order in the first two innings and four of the first six.
"He should have three more wins than we've given him," Maddon lamented.
"That gets lost in this whole game," Leyland said. "That was huge for us. Laird was a big part of this win."
- Verlander has lasted at least eight innings eight times this season, setting a career high.
- Longoria ended an 18-game stretch without a homer.
- Sunday marked the 104th anniversary of Ty Cobb's first game in the majors. In his first at-bat on Aug. 30, 1905, Cobb doubled off New York Highlanders' ace Jack Chesbro at Detroit's Bennett Park.
- Thomas matched a season high with three hits.
- Crawford stole his 55th base, moving into a tie with Boston's Jacoby Ellsbury for the most in the majors, and is five away from setting a career high.
- The Tigers drew 36,067 fans, putting them over the 2 million mark.