The MK Dons had tested their top-flight hosts throughout the game, enjoying most of the chances, but they paid the price of some bad misses when Gabbidon powered home from a Shaun Wright-Phillips corner in the 73rd minute.
Victory hands QPR a fourth-round meeting with fellow Premier League Londoners Chelsea but their lacklustre performance gave Hughes, appointed last week, a measure of the task in hand as he aims to keep the club in the top flight.
"I think there was a lack of sharpness as a consequence of playing Sunday-Tuesday and we were a bit leggy and they were excited, but we stuck at it although we know we can play a lot better than that," said Hughes, whose first match in charge was Sunday's 1-0 league defeat by Newcastle United.
"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," he was quoted as saying by the BBC.
In another third round replay, Bolton Wanderers put aside their Premier League woes to beat League Two (fourth tier) Macclesfield Town 2-0.
Bolton, second from bottom in the Premier League, took a first-minute lead through captain Kevin Davies before midfielder Martin Petrov doubled the score in the 26th minute.
Macclesfield stepped up their game after the break but Bolton held on to record their first victory at home since November. Owen Coyle's side will meet Swansea City in the next round.
In an all-Championship (second division) replay, Jermaine Beckford scored a hat-trick as Leicester City swept aside Nottingham Forest 4-0 to book a fourth-round encounter with League Two (fourth division) Swindon Town.
There was another hat-trick and an even more comprehensive scoreline for Millwall with the Championship hosts hammering fourth tier Dagenham & Redbridge 5-0 thanks to Darius Henderson's treble and two goals from Harry Kane.
Millwall will host Championship leaders Southampton in the fourth round.
There are more third round replays on Wednesday when Premier League Wolverhampton Wanderers host Birmingham City, who were relegated from the top division last season, and Championship side Brighton & Hove Albion travel to fifth tier Wrexham.
