Mitchell scored 23 points and Releford matched his career-high with 20 to lead the Crimson Tide to a 74-67 win over New Mexico Monday night in the second round of the NIT.
The Tide (23-11), mostly known for its defense, made 15 of 20 shots in the second half to move into the quarterfinals. Alabama will host Miami on Wednesday night, aiming for its sixth trip to the NIT final four at Madison Square Garden.
"I think our guys are excited to still have an opportunity to continue to play and continue to try to play for a championship," Tide coach Anthony Grant said.
Kendall Williams led New Mexico (22-13) with 18 points, including a couple of 3-pointers in the final 35 seconds to cut it to a six-point deficit.
Then Charvez Davis hit one of two free throws with 24 seconds left to make it a three-possession game and the Lobos missed their 3-point attempt, anyway.
Davis finished with 14 points and hit half of Alabama's six 3-pointers.
Mitchell was 8-of-11 shooting while Releford, a freshman point guard, added six rebounds and six assists and frequently drove the lane.
"Trevor all year has done an outstanding job not necessarily in scoring but in getting other guys shots, doing a great job defensively," Grant said. "That's what you want to see out of your basketball team, that when the opportunity presents itself different guys step up. I think that's the mark of a good team."
Leading scorer JaMychal Green didn't score for the first 31 minutes and finished with six points and seven rebounds. He played only 20 minutes because of foul trouble.
Phillip McDonald had 12 points and Drew Gordon added 11 for New Mexico. Williams, who became the sixth freshman in the Mountain West Conference to score 400 points, and McDonald were each 4 of 9 from 3-point range. Gordon only had four rebounds, nearly seven fewer than his season average.
Alabama improved to 18-0 at Coleman Coliseum this season despite trailing at home in 11 of those, including a six-point deficit in the first half of this one.
"It's one of the better defensive teams that we've played all season long," New Mexico coach Steve Alford said. "They mix up their pressures, they back off, they come at you. They just do a really good job of keeping you off balance."
New Mexico, playing without injured guard Dairese Gary, was down only two points early in the second half before Alabama went on a 17-5 run led by a couple of highlight-reel dunks by Mitchell.
The first came on a long alley-oop pass from Senario Hillman and then he streaked to the basket to slam home a missed 3. He added a windmill dunk off a fast-break in the final minutes, but missed three of four late free throws to help New Mexico cut into a deficit that grew to 18 points in the final four minutes.
"We're not going to feel like we're out of it," Williams said. "Obviously being down  points doesn't help that confidence, but we've fought all year. If we did a better job of handling the press and keeping them out of transition we wouldn't have been in that position. But we were, and I think we did a good job of fighting out of it."
The Lobos had also managed to briefly cut the lead back to single digits earlier on a 3 by Williams with 7:34 left, but the Tide scored the next nine points on three drives and a 3-pointer by Davis to seemingly put the game away.
Alabama, which used the full-court press effectively at times, forced three straight turnovers to start the run.
"They're hitting shots on top of it," Williams said. "It all kind of spawned from turnovers and it gave them confidence to hit outside jumpers."
Alabama made only 11 of 23 free throws in the second half to help New Mexico hang in.
Releford had scored the final five points of the first half to give Alabama a 30-26 lead. He hit a jumper to put the Tide ahead and added a contested 3-pointer with 11 seconds left and the shot clock dwindling down.
"That happens with an inexperienced group," Alford said. "I think you really felt the effects of our first road game without Dairese. I think you really saw that at the end of the first half."