Rooney also missed a second-half penalty – the fifth time United have failed from the spot this season – as United survived a spirited second-half rally from West Ham.
The England striker was devastated when his wife's 14-year-old sister Rosie, a Rett syndrome sufferer, died on January 5.
And he delivered his own heartfelt tribute after stroking home Javier Hernandez's square ball after only nine minutes.
Rooney kissed his hands, looked to the sky and raised his arms as he walked back towards the halfway line.
It was his ninth goal of the season and extended a purple patch that began prior to his injury, since when Robin van Persie, Hernandez and Danny Welbeck have all impressed, underlining the strength within Sir Alex Ferguson's striking department.
But it was veteran winger Ryan Giggs who ran the show last night at Old Trafford.
The Welshman exploited the vast gaps to produce a virtuoso display that made him look far younger than 39.
West Ham rarely looked like troubling United, apart from brief glimpses in the second half.
United should have sealed their fourth-round spot after Jordan Spence handled Giggs' cross near the end.
Rooney, though, blazed over, the effort sailing so high neither he nor his manager, looked like they could quite believe it.
But United had done enough to seal their place.
Meanwhile, Jack Wilshere's 20-yard wonder strike finally shook off Swansea with four minutes left at the Emirates Stadium as Arsenal won 1-0.
Wilshere said: "I don't know if I'll ever hit another one like that in my life.
"It was a great set-up from Olivier Giroud.
"We know what the FA Cup means in England.
"It's a great competition. We wanted to be in the next round, but we've got a tough game away to Brighton."