City's 3-1 defeat at St Mary's meant United knew a win on Sunday would take them 12 points clear of their fierce rivals in the Premier League table with 12 games remaining.
Despite the temptation to rest players ahead of Wednesday's UEFA Champions League last 16 first-leg tie at Real Madrid, Ferguson selected a strong side and was rewarded with a 2-0 win over the Toffees.
When asked if he changed his mind over his starting line-up, Ferguson told Sky Sports: "Yes I did. I thought I'd make seven changes but when the City result happened yesterday I thought it would be a more important game today for us because it gives us a comfortable lead.
"We knew if we got a result today it would put us in a fantastic position. We can make changes later in the season."
Ryan Giggs was selected by Ferguson and rewarded his manager with an impressive display and the first goal to set United on the path to victory, meaning he has now scored in every season of the Premier League.
When asked about Giggs, Ferguson responded: "We've used up all the superlatives. He doesn't need any himself because his legacy lives on. He is a fantastic human being. At 39 years of age he is up and down that pitch all day and has fantastic energy. It is great to see."
Last season, United threw away a 4-2 lead late in the game to draw 4-4 with Everton at Old Trafford but Ferguson was pleased to see his side initially overcome a positive start from the Toffees before closing out the win.
"I thought for 20 minutes Everton dominated. They had possession and a couple of chances and were a threat from them with good delivery from (Leighton) Baines," said Ferguson.
"We saw that through and in the second half played much better without scoring the goals.
"They must remember bad experiences and that was one last year. In the last 15 minutes they showed a steely determination to make sure nothing happened."
After losing the title to City last term, there has been a keen desire for the Red Devils to regain their superiority.
And Everton boss David Moyes is not alone in believing that is what will happen.
"I think 12 points against a club like Manchester United is a big gap to make up," said Moyes.
"Football doesn't always go the way it is meant to be but it looks a lot.
"To be that amount of points ahead is a big thing at this time of the season."
Another to think United are already champions is Ray Wilkins who told Sky Sports HD that the endeavour of the club's players and the passion of their manager will ensure they seize league silverware in May.
"Mathematics always creeps into it, but the desire and work ethic they have, which is what beat a dogged Everton side, should pull them through," Wilkins said of United, who squandered an eight-point lead with six games remaining of last term to see themselves overhauled by City.
"They are a very talented group of guys but when they graft like that it makes it very difficult for the opposition - and Sir Alex really wants to wrestle the title back.
"He doesn't want the guys across the road to be the kingpins and, for that reason, I think he classed this game against Everton as more important than the Real Madrid game on Wednesday, though that will be a classic encounter."