It was the hosts who opened the scoring on twelve minutes, with Jamille Matt touching in a Delfouneso cross.
Kurtis Guthrie equalised five minutes later, side footing home after Chris Porter's effort was blocked.
The two sides couldn't be separated in the second half and the scores stayed level.
There was drama at the end, as Eastman's injury put the U's down to ten men, before Sean Murray was sent off in injury time.
The nine men held on though, and the points were shared.
John McGreal made two changes to his starting eleven, with Owen Garvan and Matt Briggs coming in for injured duo Drey Wright and Brennan Dickenson.
Garvan had missed just the Exeter game but Briggs was in the U’s side for the first time since the final game of last season.
The home side started the better, and had the first sight of goal when former U’s defender Tom Aldred headed straight at Sam Walker.
It was another six minutes until Blackpool’s next chance, but it was a chance that they capitalised on.
Delfouneso got free on the right, cut back onto his left to cross, and strike partner Jamille Matt looked like he got a touch before Tom Eastman to open the scoring.
Delfouneso then had an effort of his own, striking straight at Walker in the U’s goal.
With their tails up, the home side were getting forward at will and Matt had a volley saved on sixteen minutes.
A minute later though, the U’s were level – somewhat against the run of play.
Matt Briggs’s long range effort was superbly tipped over by Slocombe but the home keeper could do nothing to stop the U’s scoring from the Owen Garvan corner.
Chris Porter had a shot blocked but the loose ball fell to Guthrie, who couldn’t really miss from close range to make it 1-1.
Porter got on the end of a Craig Slater cross a couple of minutes later, but his flick at the near post could only find Tangerines’ keeper Slocombe.
The hosts then regained control of the game and started to put the U’s under pressure.
Brad Potts, who was finding plenty of space in behind the U’s midfield, had a couple of chances in quick succession, but the first was deflected wide and the second went wide of its own accord.
Wing back Jim McAlister got in on the act next, but his shot was easy for Walker.
The two sides then exchanged chances within seconds of each other, Potts’ shot being blocked before Slater volleyed just wide at the other end.
Dangerman Potts then had another chance, but blasted inches over the top with an angled shot – before the U’s had the final chance of an entertaining half of football.
Another Garvan corner caused havoc in the Blackpool box and Slocombe had to make a goal saving save from George Elokobi.
The ball went straight up in the air, and when it dropped just in front of the goal, Porter’s header hit the bar and went safe.
The half time whistle went seconds later, with the hosts having the better of things, but the U’s could well have gone in a goal ahead.
Blackpool didn’t let that fact affect them at the start of the second half though, they were out of the blocks quick again and should have been ahead within a minute of the restart.
Walker came for a cross but let it drop under pressure from Matt and sub Colin Daniel completely missed the ball as he attempted a volley at goal with his first touch since his introduction at half time.
Two further efforts went wide of Walker’s goal before the clock had ticked past fifty minutes, with Jordan Flores and Delfouneso guilty of missing the target.
Just before the hour mark, George Elokobi volleyed wide when he had time to pick a spot after Garvan’s free kick fell to him just inside the box.
McGreal gave Sean Murray his U’s debut on sixty four minutes, with the former Watford midfielder replacing Slater.
It gave the U’s a boost, and they looked to get forward more in the final quarter of the game.
From a long ball down the channel, Porter knocked down to Guthrie but a defender was on hand to block the effort on goal from the U’s top scorer.
With sixteen minutes left on the clock, Aldred should have scored against his old club, but headed wide from a corner when he was in enough space to at least hit the target.
Having provided the ammunition for most of the U’s chances, Garvan created a chance for himself a minute later.
The ball fell to him twenty five yards out, he teed it up onto his left foot but his goalbound volley was blocked before it could test Slocombe.
Murray, who was proving to be a nuisance to the home side, got on the end of another Porter flick, but couldn’t keep his shot under the bar.
McGreal went looking for an equaliser with ten minutes remaining, putting on fresh legs in Kane Vincent-Young, Richard Brindley made way), and replacing Guthrie with Denny Johnstone.
They both had to be more wary of defensive duties late on though, as the U’s were reduced to ten and then nine men.
Tom Eastman fell awkwardly and couldn’t continue, Porter slotting into the right centre half position, and then debutant Murray received his marching orders.
He was in possession but on the difficult pitch, the ball ran away and he unfortunately caught McAlister who had read the danger well.
The red card was produced and the stricken Blackpool wing back was stretchered off looking in a great deal of pain.
Despite the two man advantage, the hosts couldn’t break through and the final whistle went with the scores level at 1-1.
The hosts certainly had the better of the possession and territory, but clear cut chances were there for the U’s – all things considered though, it was a hard earned point to take back to north Essex.