Paul Jewell's side appeared to have done enough to snap their five-game winless streak after Angel Martinez's own goal and Tommy Smith's second-half strike.
But Grandin brought the visitors back into the match, scoring their first just three minutes after he had been brought on, and he set up Phillips for his eighth goal of the season to ensure they left Suffolk with a point.
Phillips then missed a glorious chance to win it but Ipswich held on to move four points clear of the npower Championship relegation zone.
The Tractor Boys did not allow their recent slump in form to disrupt their attacking intentions early on and they led after just 10 minutes.
Jason Scotland started the move by flicking the ball out to Lee Martin before driving into the box, determined to meet the winger's cross.
His inviting delivery was sent Scotland's way but Martinez reached the ball first, only to glance his header into the corner of his own net.
That goal gave the hosts confidence and Josh Carson came within a whisker of adding a second but his clever lob dropped agonisingly wide of Blackpool goalkeeper Mark Howard's goal.
The visitors' three-man attack was often starved of service but Lomana LuaLua only had himself to blame when he sliced Stephen Crainey's first-time cross wide.
They suffered a blow in the opening exchanges of the second half when LuaLua was forced off with a hamstring injury and it got worse for them on the hour mark when Smith headed home his first goal of the season.
Jay Emmanuel-Thomas was instrumental in the build-up, breezing past players on the right wing before teeing up Andy Drury to pick out Smith at the back post, and the defender planted his header into the top corner.
But the visitors were given a lifeline five minutes later when a lapse in concentration from Ipswich's defence allowed Grandin to reduce the deficit.
Nobody in a blue shirt picked up Phillips from Neal Eardley's cross and Grandin was left with a simple finish after goalkeeper Alex McCarthy spilled Phillips' header into his path.
Ipswich pressed for a third goal and were caught on the counter-attack. Grandin picked out Phillips in the middle of the penalty area and he smashed the ball into the net with the outside of his foot 10 minutes from time.
McCarthy may feel he could have done more with Phillips' leveller but he redeemed himself shortly afterwards when he denied the veteran striker after he had beaten the offside trap.