United are six points clear with two games left so a point at Blackburn next weekend will secure a record-breaking 19th league championship.
"It's not mathematically over but we're nearly there," said Giggs, who immediately committed the Red Devils to going for the win at Ewood Park.
The 37-year-old told Sky Sports: "That's what we'll try to do.
"It will be a great atmosphere and, as always, we won't go for the draw, we'll go for the win."
If United secure the title, they will surpass the English record of 18 league titles they jointly hold with Liverpool.
Giggs added: "It's a great achievement by the team and by the manager to haul back our biggest rivals."
Frank Lampard pulled a goal back for Chelsea in the 68th minute but Sir Alex Ferguson's side held on for the win.
Ferguson was delighted with his side's performance, despite the nerves engendered by Lampard's goal.
"We could've scored six in the second half, but we expected a tough game and we got a tough game," the Scot told Sky Sports 1.
"We were brilliant - we got a great start but Cech made some fantastic saves.
"When we gave the ball away for their goal, we were a bit nervy but the fans helped us.
"We kept making chances and Rooney could've scored six today."
With the title all-but secured, Ferguson was happy to revel in the plaudits.
"It's fantastic to be the most successful team in the country," he said. "The minute we won that first title in 1992 the door opened, and we've been involved in the first two all throughout that period - it's a fantastic achievement.
"For the last 17 or 18 years it's been Arsenal and Chelsea as our nearest challengers, and the last few years it's been Chelsea. Arsenal made a great attempt this year but them losing today has finalised it.
"We deserve the title and hopefully we'll get that point now."
To miss out now would take a collapse of the magnitude witnessed in the 1956 Grand National - an incident Ferguson was desperate not to be reminded of.
"Don't even mention Devon Loch - my dad backed that!" he quipped.
Opposite number Carlo Ancelotti admitted his side had given themselves an uphill battle from the start.
"In the first minute we lost the game, we started so badly," he told Sky Sports 1. "It was very difficult after that to come back and try to win. The second half was better but United played better and deserved to win.
"We have to accept the defeat, today United were better and in general this season they were better than us. They deserve to win title, they will win and we have to try to maintain second place."
Defender David Luiz was culpable as Hernandez burst through to open the scoring with 36 seconds on the clock, and was substituted at half-time after receiving angry looks from Ancelotti.
The Italian was more conciliatory after the game, though, and said: "He had a little (injury) problem yesterday in training, we tried this morning and he said it was okay so I put him on the pitch.
"On the pitch, you can make a mistake."
Talk will now turn to Ancelotti's future at the club but he said: "We have to wait two weeks - it is not a long time.
"I hope to stay but it is not my decision."