A powerful Danny Gabbidon header settled a scrappy game at Loftus Road, with QPR now advancing to a dream tie against west London neighbours Chelsea in the fourth round later this month.
But Rangers, who had forced a replay with a late equaliser in the first meeting between the clubs, were made to work all the way for a win which exposed the scale of the task facing new manager Hughes.
Gabbidon’s winner came against the run of play on 73 minutes, the Welsh defender rising to meet Shaun Wright-Phillips’ corner with a firm header which flew past Dons keeper David Martin.
It was the first time QPR have reached the FA Cup fourth round since 2001, and only the club’s second home win of the 2011/2012 campaign.
“I think there was a lack of sharpness as a consequence of playing Sunday and Tuesday — we looked a bit leggy at times, but we stuck at it and in the end we got our noses in front and were able to close it out,” Hughes said.
“But we know we can play a lot better than that. I’ve seen things in the two games that have pleased me. But there are areas where we need to improve and improve quickly.
“Given the run the team has been on, perhaps there is a lack of confidence in each other. The desire is there for everyone to see, but we can improve.”
Elsewhere, relegation-threatened Premier League side Bolton had little difficulty in dispatching League Two outfit Macclesfield, from the fourth tier of English football, with a 2-0 win at the Reebok Stadium.
Macclesfield had come within a whisker of a famous upset when the first meeting between the two sides ended in a 2-2 draw, but Wanderers were in no mood for a repeat performance in Tuesday’s replay.
Kevin Davies put Bolton 1-0 up with a goal in the first minute before Martin Petrov extended Bolton’ lead on 26 minutes. Bolton will now play Swansea in the fourth round.
Leicester cruised to a comfortable 4-0 victory over fellow Championship side Nottingham Forest, Jermaine Beckford netting a hat-trick as the Foxes advanced to a fourth round meeting with Swindon.
Leicester were set on the path to victory after an own goal from George Boateng after only seven minutes following a low cross from Lloyd Dyer.
Beckford made it 2-0 on the half hour mark, heading in off the underside of the bar after a swift break out left Forest struggling to cover.
Beckford then scored two goals in seven minutes to complete his hat-trick early in the second half as Leicester piled on the agony for Forest, who are currently languishing in the Championship relegation zone.
Millwall meanwhile bounced back from their 6-0 home drubbing by Birmingham last weekend with a 5-0 win over League Two side Dagenham & Redbridge, Darius Henderson grabbing a hat-trick.
Henderson opened the scoring for the Lions on seven minutes before Tottenham loan player Harry Kane effectively settled the contest in Millwall’s favour with a 20-yard effort near half-time to make it 2-0.
Henderson added a third on 59 minutes and then coolly slotted home a penalty four minutes later to seal his hat-trick and make it 4-0.
Kane then bagged his second of the night, and Millwall’s fifth, on 65 minutes as the rout continued.
Millwall’s reward for the victory is a fourth round tie at home to Championship pace-setters Southampton.