With runners on first and second, Texas left fielder David Murphy hit a dribbler that rolled approximately one foot in front of home plate.
The play was ruled dead by Danley despite replays showing that it should have been called a fair ball. The second out of the frame was negated and eventually led to an additional two runs in Tampa Bay's 8-6 loss in Game 2.
"It's a ground ball," Rays catcher Kelly Shoppach said. "I didn't see a replay, I didn't see anything, but I was there for it.
"[Danley] said that it hit his bat on the back swing, which would have made it a dead ball. It just got messed up -- I don't know what was happening, but I know that he hit the ball. ... He made the call, and that's what he went with."
Tampa Bay manager Joe Maddon came out to briefly argue the call, while starter James Shields and Shoppach converged near the home-plate umpire.
Shields, who had already surrendered three runs in the inning, showed the ball to Danley in an attempt to prove the call was wrong, but it was to no avail.
"If it had hit the bat [a second time], it probably would have had a black scuff mark on it, but it didn't have anything but dirt," Shields said. "We get the guy out right there, I get the ground ball ... next thing you know, it [stays] 3-3."
The call stood and the second out of the frame was negated. Murphy's at-bat continued, and a wild pitch allowed the runners to move up to second and third.
To make matters worse for the Rays, Shields eventually got Murphy to strike out swinging at a curveball in the dirt, but the ball bounced away from Shoppach. The fourth run of the inning scored while Murphy safely reached first base.
It was the second wild pitch in the same at-bat for Shields, who threw just four the entire 2011 season.
"In the scorebook, I guess it's called a wild pitch, but I felt I made a pretty good pitch right there," Shields said. "I struck him out, I did my job, but unfortunately it took a bad hop.
"I think Shop kind of got blocked by the umpire a little bit on that play, but it's just the way it goes sometimes. You get some bad breaks."
When the inning came to an end, Shields had thrown 35 pitches and allowed five runs on three singles, two hit batters and a pair of wild pitches.
It was the third time this year Shields gave up four or more runs in an inning. All three came in AL West parks -- June 2 at Seattle and July 27 at Oakland were the others.
The veteran hurler remained in the game until the sixth, when he departed with runners on first and second and nobody out. He was charged with seven runs on eight hits while striking out six.
Texas now heads to Tampa Bay with the ALDS evened at one game each, and it can point to the crucial rally in the fourth as being the main reason why.
"We've done it all year," said Rangers catcher Mike Napoli, who hit a key two-run single in the fourth. "We scrap away at runs, and we play good team baseball and we do it together. We do good things, and that inning showed it.
"We all did it together, put some good at-bats together and got it done."