Alex Oxlade-Chamberlain also scored twice as Arsene Wenger saw his team close to just two points behind fourth-placed Chelsea.
Dutchman Van Persie fired the Gunners ahead inside two minutes, but a fine free-kick from Morten Gamst Pedersen brought Blackburn level.
Arsenal were soon back in front through skipper Van Persie, before Oxlade-Chamberlain extended the lead.
Gael Givet saw red for a two-footed challenge on Van Persie, and there was no way back for Rovers.
Arsenal dominated the second half, as Mikel Arteta and the impressive Oxlade-Chamberlain were both on target with Van Persie collecting the matchball following a neat near-post finish just after the hour.
Substitute Thierry Henry swept home goal number seven in stoppage time to cap a memorable afternoon at Emirates Stadium.
The Gunners, who are up into fifth place, will be hoping for a Manchester United win at Stamford Bridge on Sunday to improve their Champions League prospects for next season.
On Saturday, Wenger's side took just one minute and 19 seconds to move ahead.
Theo Walcott was played into the right side of the penalty area by Francis Coquelin after a cross was only half cleared.
The England winger, frequently maligned for his poor choice of final ball, played a low centre through the six-yard box to Van Persie who tapped in his 121st Arsenal goal to overtake Dennis Bergkamp on the all-time list.
The match had been brought forward to a 1pm start because of disruptions to the London Underground network, and there were plenty of empty seats around Emirates Stadium.
Arsenal, who had not recorded a league win in 2012, continued to press as the visitors, unbeaten in three away games including a shock win at Old Trafford, defended deep with two banks of four.
Paul Robinson turned a curling effort from Czech midfielder Tomas Rosicky around the post.
But after 31 minutes, Laurent Koscielny bundled over Anthony Modeste just outside the Arsenal penalty area.
It proved a costly foul as Gamst Pedersen whipped the resulting free-kick over the wall and into the top-left corner, a shot which Wojciech Szczesny got a hand to but could not keep out.
After the restart, there was a stoppage when Blackburn's Jason Lowe went over on his ankle in a sliding challenge from Rosicky, and the midfielder was replaced by Bradley Orr to make his debut.
Arsenal were ahead again after 38 minutes, and again it was Walcott who was the provider.
Following patient build-up, Alex Song slipped the England man away down the right again, and he sprinted to cut the ball back from the goalline right into the path of Van Persie, who again made no mistake from a yard out.
Before Rovers could regroup, it was 3-1.
Walcott and Van Persie combined again, this time to release Oxlade-Chamberlain into the Blackburn penalty area, where he skipped around Robinson and slotted home his first Premier League goal five minutes from half-time.
The afternoon got worse for the visitors after 43 minutes when Givet was shown a straight red card by referee Andre Marriner for jumping in with two feet on Van Persie.
Rovers made an immediate tactical change as midfielder David Dunn was replaced by defender Grant Hanley.
The hosts went close again when Thomas Vermaelen crashed the ball against the far post from Arteta's floated cross.
Arsenal further extended their lead after 51 minutes.
Blackburn only half cleared a corner to the edge of the area, from where Spaniard midfielder Arteta drilled the ball back into the bottom left corner.
Rovers, who had beaten the Gunners 4-3 at Ewood Park in September, were over-run again after 54 minutes when Walcott's mazy dribble through the penalty area took him past five defenders before slipping in Oxlade-Chamberlain, who turned his marker and rolled the ball past Robinson.
It was now very much a case of damage limitation for the visitors, manager Steve Kean pensively looking on from the dugout.
Van Persie, who twice struck the woodwork in Wednesday night's frustrating goalless draw at Bolton, completed his hat-trick after 62 minutes when he clipped home a cross from Coquelin at the near post.
Oxlade-Chamberlain was replaced by Henry for the final 23 minutes, which could not finish soon enough for Blackburn.
To round the scoring off, Henry - on loan from New York Red Bulls - swept home number seven in stoppage time, with the aid of a deflection.