The Lynx (6-1, 1-0) tied the match in the 19th minute when Jordan Wood fought through a logjam in front of the Centre goal to put the ball in off a Nick Frankel assist.
Rhodes got the game-winner from Ken Bode in the 39th minute on an unassisted breakaway when his shot got past Centre goalkeeper Chris Creger.
Centre took six shots in each half, while Rhodes' two first-half goals came on just three shots. The Lynx had 10 shot attempts in the second half.
Burch tried to find emotion and intensity
Burch used several reserves, trying to get a combination on the field that would play with some emotion and intensity. Instead, the Colonels fell flat.
"It's not a black and white thing," Burch said. "It's not certain players; the group as a whole has to come out and do certain things and for whatever reason, mentally, we're not doing those things.
"This game is instant feedback. We saw here today that we're not ready to play in a big game. Can we? Yeah. But I think it's just a mental decision on the players' part. We've got everything in place to be a good, good team."
The Colonels have depth, talent and a good mix of experience and youthfulness. But Friday's loss to Rhodes dealt them a harsh blow in the SCAC race.
Burch said his team will have to start the run to a title with Hendrix today. The Centre coach said his team will have to win eight straight games to have a chance, but that the Colonels are trying to break through the malaise and questions that are following them.
"We think we should be in the (NCAA) tournament. We're built for it," Burch said. "We did everything right. We're just not getting the results.
"We did it in the recruiting, we did it in the organization, we do it in our practice setting environment, I absolutely love our schedule ... I really think we've done a good job. I think it's now up to the players to go out and do it. I don't think there's anything else we can do. They've worked hard too. Everyone's done what they're supposed to do, but I think right now we're just thinking, 'How do we take this great thing we have and run with it?'"
Centre women tie 0-0
The Colonels played what coach Jay Hoffman termed "as even of a game as you could ever watch," and came out with a 0-0 tie after 110 minutes.
Rhodes held a 16-14 shot advantage, Centre keeper Erin Haney had eight saves to Rhodes' seven, and each team committed 14 fouls.
Hoffman credited his defense with picking up the first shutout of the season for the Colonels (1-2-2).
"I really think this game will gives us some confidence," Hoffman said.
Hoffman singled out Laura Heil, saying she played a very good game, and Kim Lacy, saying she had her best game of the season and narrowly missed the game-winning goal in overtime.