His seventh-minute effort took his United tally to 249 since joining the 12-times cup winners in 2004, but Rooney failed to surpass Charlton's long-standing mark as Anthony Martial and two late goals from Marcus Rashford completed United's comfortable victory at Old Trafford.
"I think it's just a question of time to score one more goal... It's arriving," United manager Jose Mourinho said after his side's eighth straight win in all competitions.
Premier League champions Leicester City enjoyed some respite from a poor campaign as they claimed a first away victory in domestic competitions this season with Ahmed Musa scoring twice in a 2-1 victory at Everton.
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Surprises were in short supply on one of the standout days in the English soccer calendar but five top flight clubs departed, three at the hands of lower league sides.
Tony Pulis's West Bromwich Albion - eighth in the Premier League - were beaten by Championship (second tier) side Derby County 2-1 at home while his former club Stoke City lost 2-0 at home to Championship Wolverhampton Wanderers. League One (third tier) club Millwall humbled top-flight Bournemouth 3-0
Darren Bent equalised for Derby before Tom Ince won it with a free kick to the delight of manager Steve McClaren.
"What a game. It was a real old-fashioned cup tie," said McClaren. "I thought that we showed great composure."
This year's lowest-ranked survivors, seventh-tier Stourbridge, suffered a disappointing end to their journey as they lost 2-1 at League Two Wycombe Wanderers. Lincoln City, who now play in the National League, gave former cup winners Ipswich Town a fright, twice taking the lead before settling for a 2-2 draw at Portman Road where they were roared on by 5,000 visiting fans.
Former England manager Sam Allardyce is still waiting for his first win since taking charge of Premier League strugglers Crystal Palace after his side drew 0-0 at Bolton Wanderers where he spent eight years in charge.
In a battle between two managers named by relegation-threatened Premier League clubs this week, Marco Silva began his tenure at bottom side Hull City with a 2-0 win over Swansea City for whom Paul Clement picked the side for the first time.
Two former cup winners, Sunderland and Southampton, require replays after draws yesterday.
Sunderland were held 0-0 by Premier League rivals Burnley while Southampton were frustrated when Norwich City equalised in stoppage time for a 2-2 draw.
Arsenal had to come from behind to win 2-1 at second-tier Preston North End.
Chelsea hosts third-tier Peterborough today.
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