The League 2 side were the better of the two teams in the first half and could have led when Garry Thompson's header flew over the bar with the keeper in no-mans-land.
But Villa improved after the break and went ahead through Ciaran Clark's header before Idrissa Gana secured the win as the game entered stoppage time.
Gareth Ainsworth was able to recall Paul Hayes to the starting line-up, taking the place of Gozie Ugwu in attack in a 4-4-2 formation, while Villa boss Remi Garde made a number of changes from the side that drew 1-1 with Premier League leaders Leicester City on Saturday.
Wycombe began confidently and tried to force an early breakthrough, although the first chance fell to the Villans when Rudy Gestede headed harmlessly wide after a corner wasn’t properly cleared.
The visitors were doing well to contain their hosts and had a couple of sights of goal, with Michael Harriman lashing over and Brad Guzan collecting a dangerous cross, while Jordan Ayew drilled into the side netting at the other end.
The vociferous away fans in the North Stand Upper were on their feet when the ball fell to Sam Wood 15 yards out following a spell of sustained pressure and his snapshot was well saved away to his left by Guzan, with the rebound bouncing to eventual safety.
Villa’s fans were becoming disgruntled and were left with their hearts in their mouths shortly before the break when Brad Guzan completely missed a Joe Jacobson cross from the left, but Garry Thompson couldn’t react quickly enough to send his header downwards and instead it flew over the bar.
There were jeers and cheers at half-time with Wanderers much the happier side, and an earlier injury to Carlos Sanchez forced Remi Garde into a change at the interval with Idrissa Gana taking his place.
Villa started much better and were almost gifted a 2-on-1 chance when Joe Jacobson miscontrolled Luke O’Nien’s difficult pass but Aaron Pierre positioned himself superbly to win back possession.
Gareth Ainsworth made his first change when Matt Bloomfield came off with a knock and Stephen McGinn entered the fray, before a lung-busting run from Jordan Ayew went unrewarded when his low cross-shot ran past the post.
Then came a good period from the hosts, started when Jason McCarthy performed a heroic tackle on Scott Sinclair to win back possession by the corner flag and the ball was worked to Sam Wood inside the opposition box, but his chipped cross was headed wide by Thompson.
Villa were running out of ideas and Ashley Westwood’s wayward shot was met with howls of derision from three sides of the ground while Wycombe enjoyed their continued stifling of last year’s cup finalists.
Idrissa Gana found row Z from a similar range and Scott Sinclair hammered wide following a dangerous cross into the six-yard box, as all of a sudden the ball kept coming back into Wanderers territory from the hosts.
Only an incredible block from Aaron Pierre denied Sinclair after the ball bounced kindly for him inside the area and then Rudy Gestede couldn’t muster enough power to send his header past Ingram from the resulting corner.
A clever move at the other end resulted in Garry Thompson dragging his left-footed shot wide from 20 yards, before Gana again shot wide and Remi Garde swapped Carles Gil for Jack Grealish while Aaron Amadi-Holloway replaced Paul Hayes up front for Wycombe.
But the breakthrough came two minutes later when Villa retained possession around the Wycombe box and Ashley Westwood floated in an inch-perfect cross for Ciaran Clark to send a bullet header past Ingram from eight yards out.
More excellent defending from Pierre denied them a second on the counter-attack moments later when Rudy Gestede broke into the box, before Gozie Ugwu was brought into the fold in place of Garry Thompson.
But Villa had developed a new-found resilence and made it difficult for their opponents to enjoy any real possession in their half, managing long balls relatively comfortably as they slowed the game down on the way to victory.
And their path into round four was secured as the clock struck 90 when Gestede laid the ball off inside the box for Gana to stroke it neatly into the far corner, ending hopes of a late fightback from the Wanderers.
Aston Villa will meet Manchester City in the fourth round of the Emirates FA Cup but for Wycombe, it’s a return to the bread and butter of the league and a meeting with Leyton Orient at Adams Park on Saturday.
Wycombe: Ingram, McCarthy, Jacobson, Stewart, Pierre, Harriman, O’Nien, Bloomfield (McGinn 53), Wood, Thompson (Ugwu 80), Hayes (Amadi-Holloway 73).
Unused subs: Lynch, Jombati, Bean, Udumaga.
Aston Villa: Guzan, Lyden, Richardson, Richards, Clark, Westwood, Sanchez (Gana 45), Grealish (Gil 73), Sinclair, Ayew, Gestede.
Unused subs: Bunn, Lescott, Veretout, Kozak, Cissokho.
Referee: Mr Craig Pawson