The 39-year-old Welshman slotted his side in front after 13 minutes to continue his extraordinary feat of having scored in every Premier League season since the competition started 21 years ago.
Robin van Persie was also on target for United before half-time as the leaders took full advantage of champions Manchester City's shock 3-1 defeat at Southampton on Saturday.
With 12 games remaining Sir Alex Ferguson's side have 65 points, 12 more than City, and are closing in on a 20th league title.
"We've got to win our games regardless of what happens with City and if we concentrate on our own games we'll be OK," Ferguson, whose side face a huge Champions League match away to Real Madrid on Wednesday, told Sky Sports.
"I was going to make about seven changes for the game but when I saw yesterday's result I changed that because we knew if we got a result it would put us in a fantastic position."
At the other end of the table, Aston Villa claimed a vital 2-1 home victory over West Ham United to move out of the bottom three, Christian Benteke and Charles N'Zogbia the scorers.
A remarkable 4-4 draw with Everton in the final weeks of last season's title race proved United's undoing as City pipped them on the final day on goal difference.
This time, however, there were no slip-ups from Ferguson's side as they recorded a 10th consecutive home league win.
Despite the proximity of the trip to Madrid, Ferguson resisted any temptation to rest key players - a mark of respect for an Everton side chasing a top-four finish and who beat United on the opening day of the season on Merseyside.
With Real manager Jose Mourinho watching in the stands, United produced a clinical performance, even if leading striker Van Persie was guilty of an astonishing miss early on when he took the ball past Everton keeper Tim Howard but blasted his shot against the outside of the post.
"You have to remember your bad experiences and that was one last year," Ferguson said.
"We showed a steely determination this time."
After Van Persie's miss United did not have to wait long for their opener. The Dutchman picked out Giggs with a pull back and the wily veteran steadied himself before curling a precise shot in off the post.
CLEVER PASS
Everton enjoyed spells of possession but on the stroke of half-time right-back Rafael released Van Persie with a clever reverse pass and the Dutchman again rounded Howard before shooting into the empty net despite Johnny Heitinga's desperate attempt to keep the ball out.
Van Persie's goal took his league tally for the season to 19 and he could have reached the 20-mark after the break as United played on the counter-attack.
Ferguson's side never lost control and comfortably contained Everton after the break, although David de Gea was required to make a fine low save after sloppy play by Chris Smalling allowed Nikica Jelavic a rare sight of goal.
With th
