Abou Diaby and Emmanuel Eboue put us into a commanding position at Bloomfield Road but Gary Taylor-Fletcher replied as relegation-threatened Blackpool played for their top-flight lives.
Taylor-Fletcher felt he was denied a penalty but Van Persie made victory safe after 76 minutes.
The afternoon started in dramatic fashion as Almunia injured his knee in the warm-up and Arsene Wenger was forced to turn to 41-year-old Lehmann.
It was an unexpected 200th appearance for the German, who was recently coaxed out of retirement to provide emergency cover in the title run-in.
Lehmann had little to do in the first half as we overpowered the struggling Tangerines.
Blackpool had an early chance when Ian Evatt headed over from a Charlie Adam corner but after that it appeared we had no intention of suffering a repeat of our Blackburn stalemate.
Andrey Arshavin both Van Persie put early shots over before Richard Kingson rushed out to deny Samir Nasri.
It quickly became one-way traffic and the we carved open the Blackpool defence with ease to claim a 17th-minute lead.
Fabregas picked out Van Persie with a superb cross-field ball and the Dutchman crossed for Diaby to sidefoot home from close range.
They grabbed a second just three minutes later as Eboue played a neat one-two into the box with Jack Wilshere and then blasted past Kingson.
Blackpool enjoyed a little spell of possession but were unable to test Lehmann and Van Persie had the next chance when controlled another long Fabregas pass and shot at Kingson.
Kingson needed to be alert again to block an effort by the fleet-footed Nasri after more slick football by the Gunners.
Nasri had another opportunity seconds later when the ball was lobbed back into the box by Fabregas but his volley hit the bottom of the post.
Van Persie took the ball past the outrushing Kingson to set up Diaby but Stephen Crainey got back to tackle.
Some Blackpool fans thought Adam had pulled one back immediately after the restart but his long-range free-kick had struck the side-netting.
The hosts, however, had realised they had little to lose by taking the game to us and did reply after 52 minutes.
Luke Varney was fouled but play proceeded and Jason Puncheon played in Campbell.
The striker appeared to be fouled by Lehmann as he closed in on goal but the ball ran on for Taylor-Fletcher to fire home.
Blackpool were inspired and poured forward again.
Manager Ian Holloway was furious his side were denied a penalty when Taylor-Fletcher went down under a Laurent Koscielny challenge.
Taylor-Fletcher then headed wide as Blackpool maintained the pressure but Van Persie shot across the face of goal at the other end.
We made the game safe 14 minutes from time as they quickly turned defence into attack.
Campbell shaped to shoot for Blackpool but Sebastien Squillaci won possession and Fabregas released substitute Theo Walcott down the right.
Blackpool struggled to get back and Walcott crossed low into the box and Van Persie made no mistake in front of goal.
Lehmann was required to pull off his best save a couple of minutes later when he rushed off his line to deny Campbell, who found himself one-on-one with the Gunners stopper.
Blackpool continued to try and set up a tight finish but Evatt headed at Lehmann and the we eased to the final whistle.