The 31-year-old scored in the 94th minute of the clash at the Britannia Stadium, lashing home a wonderful last-gasp free-kick to tie the scores as United looked destined for defeat.
It took him past Sir Bobby Charlton's tally of 249, set between 1956 and 1973, with Rooney having reached the record in just 546 games for the club.
Rooney arrived at Old Trafford in 2004 in a £27 million move from Everton and scored a sensational hat-trick on his debut against Fenerbahce in the Champions League. His greatest return in a single season came when scoring 34 in all competitions in the 2009-10 season, a feat he repeated in 2011-12.
Although he has found regular football more difficult to come by under Jose Mourinho this season, he will still be hoping to continue his record of having recorded double-figure goal returns in every one of his campaigns as a Manchester United player.
This is not the first time Rooney has usurped Charlton as a record holder, having also surpassed the World Cup winner's England mark of 49 goals in 2015. He has gone on to take his total to 53 at international level and now holds the rare feat of being the greatest scorer for both his club and his country.
"It's an honour and I'm very proud," he told BBC Sport after the 1-1 draw against Stoke. "It's difficult at the minute to be over pleased because of the result.
"It's two points dropped but, in the grand scheme of things, it's a huge honour for me. It's something I never expected when I joined the club but I'm delighted and I'm very proud.
"It's been a great journey, very successful and there's a lot more to come."