Demba Ba's spectacular 49th-minute volley and a stunning Petr Cech save earned Chelsea a 1-0 win at Stamford Bridge to set up a Wembley semi-final with Manchester City on April 14.
Chelsea's attentions now turn to Thursday's Europa League fixture with Rubin Kazan - their third of six games in 16 days - before Sunday's match with Sunderland in the Barclays Premier League.
The Jekyll and Hyde Blues are chasing a top-four finish and Champions League qualification next term, but that particular challenge was derailed by Southampton on Saturday before today's recovery against United.
Benitez said: "We had a turning point two weeks ago. One game (at Southampton), it seemed that everything changed.
"The race for the top four will be until the end of the season. We're in the top four with one game in hand so we're in a very good position.
"We're in the semi-finals of the FA Cup, quarter-finals of the Europa League. It's a great season, at the moment. It could be even better."
The turning point to which Benitez - unpopular at Stamford Bridge due to his prior association with Liverpool - refers was at Old Trafford in the original tie, when United raced to a 2-0 lead only for Chelsea to respond to force the replay.
In a match of few chances, Chelsea took the lead when Ba escaped the attentions of Rio Ferdinand to meet Juan Mata's lofted pass and find the top corner.
Ferdinand endured a torrid afternoon and was subject to abuse throughout. John Terry, another former England captain, was an unused substitute but also faced vitriol from the stands.
United had plenty of time to find an equaliser.
Javier Hernandez had an opportunity to level when he met a Danny Welbeck cross, but Cech was somehow able to divert the ball over.
Had Hernandez met the ball with his head, rather than his shoulder, the result might have been different.
Benitez added: "It was a great save, with a great goal."
Substitute Robin van Persie spurned two late chances as Chelsea ended United's hopes of a first FA Cup win since 2004 and a first double since the 1999 treble-winning season.
Chelsea, meanwhile, can ill afford injuries as Benitez aims to nurture his side through the crucial conclusion to the season.
The Blues next play on Thursday in the Europa League against Rubin Kazan of Russia, with left-back Ashley Cole absent with a hamstring problem.
It is doubtful whether the England defender will be fit for Wembley, while Gary Cahill (knee) is also out for a further two to three weeks, weakening Chelsea's options.
Benitez, who was pilloried for his selection against Southampton, said: "When you rotate players sometimes it can go well, sometimes not so well."
Chelsea are now within 90 minutes of a May 11 FA Cup final, with City standing in their way.
Benitez said: "It couldn't be more difficult. This year everything is so difficult. If you want to win, you have to beat the best teams.
"United is one of the best, City is another one. It's another challenge."