The England international pounced just before half-time before three own goals and a strike by Dimitar Berbatov took United to 56 points.
Liverpool overcame the dismissal of Sotiros Kyrgiakos to beat Everton 1-0 in a fierce Merseyside derby at Anfield to move into the top four for the first time since October.
Carrick struck a deflected shot past England goalkeeper David James, Bulgarian Berbatov atoned for a first-half miss with an excellent long-range strike and Marc Wilson helped Patrice Evra's pass into his own net to complete the rout.
"It took us a while to get the first goal but we had a lot of pressure, a lot of possession and we were patient enough," United mananger Alex Ferguson told MUTV.
"I think that's important, especially when teams come and sit there, like they did today. We were fortunate with the second one, but that was important. It opened the game for us and in the second half we had a good peformance."
Visiting manager Roberto Mancini was left rueing his side's failure to match Hull's determination and said they must change their mental approach on the road to secure a top four finish.
"Hull were more aggressive but if you understand why you lost sometimes it's better. We must change our mentality and play away games like we play at home," the Italian told Sky Sports.
