Ian Holloway's side had come from a goal down to win their past three league encounters, but could not find the winner on this occasion after Stephen Crainey's second-half free-kick cancelled out Erik Huseklepp's opener for the visitors.
The Seasiders dominated possession for long periods, but Huseklepp - who scored an injury-time winner when the two sides met at Fratton Park in September - spurned a series of opportunities to put the result beyond doubt after the interval.
Blackpool passed up the chance to go third in the Championship, while Portsmouth edged 10 points clear of the bottom three.
On-loan West Brom striker Roman Bednar made his first start for the hosts in one of five changes from the midweek FA Cup victory over Sheffield Wednesday.
Clear-cut chances were at a premium in the opening exchanges as Huseklepp dragged a speculative volley wide and Bednar headed over from Lomana LuaLua's cross at the other end.
In the 20th minute Blackpool had the ball in the net, but LuaLua's free-kick from the left flank was correctly ruled out for offside as Chris Basham flashed his boot at the ball before it went past Pompey goalkeeper Stephen Henderson.
The contest was heating up, and after Basham got on the end of some good work from LuaLua to drill wide from the edge of the area, Blackpool goalkeeper Matt Gilks got the better of Huseklepp in a one-on-one.
The Norwegian was first to the loose ball though, and Marko Futacs headed over from his chipped cross.
Portsmouth took the lead on the stroke of half-time when Kelvin Etuhu took advantage of a static Blackpool defence to fire goalwards on the angle. Gilks parried clear but Futacs steered back towards the danger area for Huseklepp to produce an assured finish on the turn.
Blackpool were furious, claiming LuaLua was fouled in the build-up to the goal, and Tom Ince arched a shot narrowly wide from distance as they sought a response in the opening minute of the second half.
But Pompey were still carrying a considerable threat and Huseklepp's touch let him down as he burst between the Tangerines' centre-backs in the 52nd minute, moments before Futacs expertly spun Craig Cathcart and stabbed against the outside of the post from 20 yards.
Full-back Alex Baptiste teed himself up to volley over as Blackpool kept the pressure on with the hour approaching, but Huseklepp soon passed up another clear opening.
After springing the offside trap and racing into space down the right channel, the attacker contrived to thrash a simple cross out of play with Futacs and Etuhu poised to double Portsmouth's lead.
A speculative 72nd minute effort from Blackpool substitute Gary Taylor-Fletcher was off target and once again followed by Huseklepp bursting into the home box, but Gilks got behind a shot that lacked purchase.
Huseklepp was eventually made to pay for his second-half profligacy as former Southampton full-back Crainey curled a sumptuous free-kick into the top corner after Greg Halford fouled Baptiste in the 75th minute.
There was almost more late drama from Holloway's men but Henderson produced a fine save from a stinging volley by substitute Ludovic Sylvestre to preserve a point for Pompey.