Juan Mata's deflected strike three minutes from time gave the Blues a 1-0 win over a below-par United at Old Trafford and restored their advantage over Tottenham and Arsenal in the Barclays Premier League.
Benitez's men, who have a healthy advantage on goal difference, can now effectively secure a top-four spot with victory over Spurs at Stamford Bridge in midweek.
The Blues' interim manager said: "It is massive for us.
"We knew that we have to get six or seven points to guarantee the top four and we have got three points here. Now we play against Tottenham and we are in the driving seat."
Chelsea had the upper hand throughout against a United side who appeared to have let their intensity levels drop after securing their 20th domestic title.
They still did enough to frustrate the Londoners but even though a draw would have been a good result for the visitors, Benitez claimed he did not want to settle for 0-0.
He said: "When the goal came we were really pleased and convinced it was an important step forward.
"Obviously United, after winning the title, normally you can expect they are a little bit more relaxed.
"My team talk at half-time was trying to increase the tempo because I could see we were controlling, doing well but were still missing the high tempo that is necessary if you want to beat a team like United. I think we did it in the second half. It still wasn't perfect but enough for winning the game."