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."
Goalkeeper Petr Cech echoed his boss' sentiments, especially after seeing both north London sides record victories on Saturday over Southampton and QPR.
"It was a massive moment," Cech told Sky Sports 1.
"After the results yesterday [both Arsenal and Tottenham won on Saturday], we knew we had to win.
"We have a massive game and we go into the game three ahead - if we win we leave them behind, it changed the preparation for Wednesday."
It was Mata's 19th goal of the season and the Spaniard is hopeful the strike will be a catalyst for his side to secure a Champions League place for next season.
"It was an important victory, it was like a final.
"We have another great game next week we have to win and aim to get third.
"I'm scoring more goals than ever. I'm really happy, I want to keep scoring, keep assisting and keep helping the team.
"We have three more games to play, we want to win as many as we can.
"We deserve to play in the Champions League next season.
"If we play together like today [Sunday] we can do it."
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."
Former Liverpool manager Benitez remains a controversial and unpopular choice of manager at Stamford Bridge and is destined to leave the club at the end of the season.
Yet despite continuing to suffer abuse from Chelsea fans, he is close to securing the tangible success of a Champions League spot and a trophy in the Europa League.
He said: "I don't want repeat and repeat the same things - with all the circumstances around the games, the squad we have not being too big, Africa Cup of Nations, Japan - you put everything together, and we are still there, doing well, with a lot of semi-finals and final in the Club World Cup.
"It is what we had to do and we are doing that."
Benitez was an animated figure throughout on the touchline and appears to be relishing the remaining days he has in the job.
He said: "I have to do my job until the end of the season and I will do it.
"I am a professional. I will try to concentrate on that. The other things are not my decision.
"When I came here I was convinced we could do really well.
"In January I was expecting some surprises but they didn't come so we have to carry on and keep working harder.
"We now just have to try to bring the best from our players."
Benitez confirmed playmaker Eden Hazard missed the game with a calf injury and will be assessed before the Tottenham match.