With Real Madrid manager Jose Mourinho watching from the directors' box at Old Trafford ahead of his team's Champions League tie against Alex Ferguson's side at the Bernabeu on Wednesday, United took full advantage of second placed Manchester City's surprise defeat at Southampton on Saturday.
Giggs opened the scoring early on with his first league goal of the season, maintaining his astonishing record of having scored a league goal in each of his 23 seasons as a United player, a sequence which now covers every year in Premier League history.
Van Persie got the second just before the break and, with City stumbling of late, the destiny of the title is firmly in United's hands once again.
United should have taken the lead after 10 minutes and would have done so but for an uncharacteristic error by the prolific van Persie, who collected Wayne Rooney's through ball and rounded goalkeeper Tim Howard only to hit the outside of the post as he attempted to convert.
It was a rare slip by a forward just two goals shy of the 20-league goal barrier, but it did not take the Dutchman long to make amends as he set up Giggs for a 13th minute opening goal.
Antonio Valencia out-jumped Leighton Baines to head on a long ball from Jonny Evans which van Persie collected. His pass was perfect for Giggs, who had the time to steady himself before clinically placing the ball past Howard.
In response, until Leon Osman's weak, off-balance shot dribbled into David de Gea's grasp after 24 minutes, Everton generated little to worry the home defence.
De Gea was required to be far more alert just before the half hour, however, when he dived acrobatically to his left to keep out an Osman volley from the edge of the area which appeared destined for the corner of the United goal.
Buoyed by their best passage of the game, Everton also asked questions of the United defence when Rafael da Silva was forced into a goal-saving challenge on Victor Anichebe, who looked poised to covert a Kevin Mirallas cross and, again, when Osman flashed a hopeful volley wide after a poor punch from de Gea.
But, on the stroke of half-time, Everton's tactic of playing a high defensive line to try and catch van Persie offside failed as Rafael played through a perfectly-weighted pass and the Dutchman timed his run superbly.
With Phil Neville playing him onside, van Persie sped away from Heitinga and rounded Howard, this time succeeding where he had failed earlier and converting despite the defender's attempt to clear off the line.
The timing of that second goal proved significant and took away the momentum Everton had been building prior to half-time.
United easily negotiated the opening 20 minutes of the second half without allowing Everton any foothold in the game and should, in fact, have extended their lead after 66 minutes.
Van Persie's right-wing corner was flicked on at the near post by Giggs and, having seen his initial header blocked by Howard, Evans had two more unsuccessful attempts to force the ball over the line.
The league leaders maintained the pressure seconds later when Tom Cleverley met a half-cleared corner and saw his 20-yard volley tipped over the bar expertly by Howard and van Persie rolled a shot wide after being set up by Giggs.
Osman looked Everton's best hope of getting off the mark with some creative midfield play but it was a mistake by United substitute Chris Smalling that let in Nikica Jelavic for an 82nd minute shot which was well saved by de Gea.
Manchester City's hopes of defending the Premier League title were dealt a major blow on a disastrous evening for the champions as Southampton secured a 3-1 victory at St Mary's on Saturday.
After Jason Puncheon opened the scoring for Mauricio Pochettino's team, an embarrassing mistake from City goalkeeper Joe Hart allowed Steven Davis to double Southampton's lead.
Edin Dzeko got one back for City but a calamitous own goal from Gareth Barry shattered Mancini's men.
For Southampton, the victory means they are now six points clear of the relegation zone and, on this evidence, look destined to secure their Premier League status for another season.
After returning from African Cup of Nations duty on Tuesday, City's Yaya Toure started his first game since the 3-0 win over Stoke on New Year's Day.
Pochettino selected an attacking line-up featuring Rickie Lambert and Jay Rodriguez and the Argentine could not have asked for a better start.
Puncheon stole the ball from Barry in the seventh minute and fed Jay Rodriguez, who saw his effort smothered by Hart.
Unfortunately for the England goalkeeper, the ball fell directly into the path of Puncheon and he slotted home from the rebound.
Things went from bad to worse for Hart midway through the half as Lambert cut in from the right flank and hit his shot straight at the goalkeeper, but the ball slipped out of his grasp and was stabbed in by the onrushing Davis.
A flashing volley from the lively Rodriguez that missed the post by inches almost extended Southampton's lead just after the half-hour mark before Pablo Zabaleta saw his curling effort just drift wide.
Less than five minutes later, the City right-back was instrumental in the counter-attack that saw City pull one back, with Dzeko converting a close-range finish.
Southampton have the unwanted record of throwing away more points from winning positions than any other Premier League team, but they should have been given the chance to restore their two-goal cushion on the stroke of half-time when Toure seemed to bring down Rodriguez, only for referee Martin Atkinson to wave their appeals away.
If City thought their luck had changed, they were sadly mistaken.
Puncheon came close to grabbing his second of the game from Lambert's cutback two minutes after the break.
But Southampton didn't have to wait long for their next goal. Within 60 seconds, Lambert again found space down the left but his ball across the face of the box appeared harmless until Barry inexplicably sidefooted past a helpless Hart.
Mancini threw on James Milner for Samir Nasri in an attempt to chase the game but once more it was the hosts who looked more likely to extend their lead.
With City still struggling to create any real chances, Maicon replaced David Silva and finally they looked a threat going forward.
Saints goalkeeper Artur Boruc did well to hold on to the ball following a goalmouth scramble, but Mancini cut a frustrated figure down on the touchline as his side continued to struggle for inspiration.
Some City fans tried to put on a brave face on things as they sang a tribute to Mancini in the dying moments, but this insipid display could end up being even more significant for the Italian's future than it is for their title prospects.