Joe Jacobson's left-footed delivery from corners always caused Villa problems, but Wycombe did not have many other bright moments in the first half.
After a quarter of an hour, Scott Wood's shot had all the power taken out of it by Jores Okore after Micah Richards had failed to track the winger, but the latter made up for his mistake with the opening goal at the other end.
Carles Gil edged into the area before stabbing the ball back to Richards and he picked out the far corner with a low shot.
Both teams were struggling to find the killer blow in the final third and Richards's strike separated them at half time. Less than three minutes into the second half, Wycombe were given a golden chance to equalise.
Referee Michael Oliver adjudged that Ashley Westwood had unfairly challenged Matt Bloomfield when contesting an aerial ball and pointed to the spot. Wycombe's stand-out player Jacobson stepped up and made no mistake from 12 yards to level the scores.
Moments later Wycombe almost turned the game on its head when Scott Wood's goalbound volley was cleared off the line by Okore.
Wycombe were able to hold on for a draw, meaning that they will be in the hat in Monday's fourth-round draw ahead of the replay at Villa Park later this month.