San Jose goalkeeper Jon Busch stopped a shot by Jeff Larentowicz and the rebound came right to Moor, who sent the ball back into the net.
"We needed that goal," Larentowicz said. "We needed a tie or a win."
Colorado (10-9-12) ended a three-game losing streak and extended its winless streak to 0-3-2. The Rapids have been held to four goals in that stretch.
"This stops the rock," Colorado coach Gary Smith of ending the losing streak. "It instills some pride again."
Chris Wondolowski scored in the 19th minute for San Jose (6-11-13), which is 0-1-2 over its last three and 0-5-4 in the last nine road games. The Earthquakes began the day six points out of 10th overall and the final playoff spot.
San Jose played without Sam Cronin, who missed the game with a yellow card accumulation.
"The game hinged on our inability to score the second goal," San Jose coach Frank Yallop said. "If it would have been 2-0 I think it would have been a lot harder for Colorado to get back into the game."
Colorado won the first meeting, 2-1, on Aug. 13 in San Jose.
The Rapids put together two scoring chances early without results.
Jamie Smith couldn't get the ball past a wall in the 13th minute. Kosuke Kimura had a wide open look from inside the box in the 17th minute, but his shot was easily grabbed by Busch.
The play led to the game's first goal on a mistake by goalkeeper Matt Pickens.
Pickens tried to undercut a shot by Khari Stephenson. Instead he sent the ball to Wondolowski, who beat Pickens from 20 yards out in the 19th minute.
It came out pretty hot," Wondolowski said of his 11th goal of the season. "It was a big rebound, but I'll take those any day."
The Earthquakes could have had a two-goal lead at halftime, but Wondolowski couldn't get the ball past Pickens in the 36th minute.
"I thought I had the near post on him and I hit a pretty bad shot," said Wondolowski. "If hindsight was 20/20, I should have gone far post."
Colorado defender Marvell Wynne denied another goal, knocking down a shot by Simon Dawkins after a turnover deep inside the Rapids' end in added time of the first half.
San Jose maintained offensive pressure as Pickens steered aside a shot from the slot by Dawkins in the 60th minute. A moment later Stephenson barely missed the right post after picking up a loose ball near midfield.
The Rapids took control in the last 21 minutes. Busch caught Moor's header in the 70th minute, and Colorado stayed on the offensive. Moor cashed in, with the game-tying goal.
"The ball popped out right in the air and it sat there for Drew," Larentowicz said. "This time he was able to pop it in."
(Copyright 2011 by The Associated Press. All Rights Reserved.)