Playing his 500th game for Manchester United, midfielder Paul Scholes scored the opener before defender Rio Ferdinand double the advantage to condemn Liverpool to their fourth defeat of the campaign.
The win was enough for Ferguson to declare the Red Devils could be crowned champions.
"There's been a growing belief since the beginning of the season. The belief that we can win it," the Scotsman said.
"We started with the hope, desire and intention to do well and so far the players haven't let anyone down. Some of our young players starting to develop very well.
"After losing to Arsenal we couldn't afford to lose another big one. The players responded to that and gave an excellent performance. I'm looking for our team to step forward and have a real go this year."
Ferguson praised the contributions of goal scorer Paul Scholes and Michael Carrick, who outplayed Liverpool in central midfield to take control of the match.
"We just tried to continue the way we've played lately. We've been playing good football," said Ferguson.
"Michael Carrick was fantastic and Paul Scholes gave a great display as well. In the big matches you need that composure and the midfield was an important component for us.
Seen as challengers for the title before the season started, Liverpool are now 11 points off the pace and in urgent need of form in front of goal.
One team with no such worries is Arsenal.
The Gunners gave manager Arsene Wenger the perfect birthday present with a 4-0 rout at Reading.
Wenger was able to celebrate his 57th birthday in style as two goals from Thierry Henry and further strikes from Aleksandr Hleb and Robin van Persie sealed a fifth successive Premiership win for the Gunners.
Wenger and Van Persie dance a
It then became a popular day for title declarations.
"I feel strongly that the hunger is there and the quality is there. It is very competive at the highest level but we believe we can do it," said Wenger.
More Hammers woe
London rivals Tottenham pushed West Ham manager Alan Pardew one step closer to the exit door when they won their derby 1-0.
Martin Jol’s side continued their revival through a goal to striker Mido, while the Hammers lie in 19th place in the table.
On Teeside, Boro manager Gareth Southgate is seeing the pressure on his post lifting with his side’s second straight victory.
Nigerian striker Aiyebeni Yakubu scored the winner in the 85th minute to pile on more misery to local rivals Newcastle.
Goalkeeper Jussi Jaaskelainen was the hero for Bolton as he saved two penalties in the final three minutes to give his side a dramatic 1-0 win over Blackburn.
Spanish midfielder Ivan Campo struck just after an hour to continue his stunning run of form to secure third place for Sam Allardyce's men.