The Seasiders dominated for large swathes of the fixture but it was the Scottish Championship side who claimed the win, courtesy of Andrew Nelson’s bizarre first-half effort.
The striker charged down Mafoumbi as he attempted to pass the ball out from the back and his block inadvertently diverted into the back of the empty Blackpool net.
The hosts had otherwise failed to trouble Blackpool, who looked tidy in possession while creating three or four good opportunities of their own.
But it was a familiar problem to last season when those chances weren’t dispatched, which will no doubt increase calls from supporters to find that all-important goalscoring number nine.
New boss Simon Grayson watched on from the stands as first-team coach Ian Dawes selected two different sides to feature in each half.
Steve Banks and Ian Miller, meanwhile, joined Dawes in the dugout ahead of their expected move to Bloomfield Road, where they will join Grayson’s backroom staff.
After a typically slow start, the type of lull that plagues most pre-season friendlies, the first opening of the game came the way of Dundee.
Unlike the Seasiders, the Scottish Championship side were playing in their final pre-season game of the summer ahead of their campaign opener on Saturday in the first round of the Scottish League Cup.
After some neat inter-play in and around the Pool box, the hosts worked the ball to attacking midfielder Paul McGowan who failed to test Christoffer Mafoumbi with his 25-yard drive, which sailed wide.
The Seasiders lined up in a 4-3-3 formation, with Liam Feeney deployed in the unusual position of right-back and Michael Nottingham in the centre of defence.
Remarkably for Blackpool there were no trialists named in their squad, something we had come to expect during the Oyston tenure.
Armand Gnanduillet, leading the line for Grayson’s men, came within a whisker of opening the scoring after just nine minutes.
The striker used his strength well to back into his marker, before spinning and producing a volley on the turn which bobbled just wide of the near post.
Pool came close on a couple of occasions in quick succession, Nathan Delfouneso seeing his cross inadvertently head towards the top corner only for Dundee keeper Jack Hamilton to palm away for a corner.
Curtis Tilt then headed wide at the back post from the subsequent corner.
Pool had some joy down their right in the early stages, with Feeney delivering some dangerous crosses into the Dundee box.
One such delivery caused some danger for Hamilton, who spilled the cross before snatching the ball at the second attempt just as Gnanduillet was ready to pounce.
The clearest chance of the half fell the way of Blackpool on the half-hour mark and it came via new signing Sullay Kaikai.
The winger, who up to that point had been quiet, cut inside from the left before producing a fierce drive that just missed the top corner.
The half appeared to be petering out until the 41st minute, when the home side took the lead in bizarre circumstances.
Christoffer Mafoumbi was punished for taking too long to play the ball out from the back and his attempted pass was charged down by striker Andrew Nelson, whose block diverted into the back of the empty net.
The Seasiders had a couple of half attempts to atone for Mafoumbi’s mistake and instantly draw level, but both Jamie Devitt and Kaikai failed to find the back of the net with their strikes from the edge of the box.
Pool made 10 changes in total at the break, Mafoumbi ironically the only man to survive despite his glaring error.
Adi Yussuf, recently returned from the African Cup of Nations, saw an early sight of goal but the striker wasn’t able to get enough contact on his glancing header, while Harry Pritchard blazed an effort high and wide.
Twenty minutes into the second period, Pool had the ball in the back of the net when Yusifu Ceesay stabbed home from close range.
However the effort was ruled out after the referee penalised Ryan Edwards for climbing on top of his marker as he headed the ball back across the face of goal.
Pool dominated in the final stages of the game and they did well up to the final third, which is where their lack of quality let them down.
Matty Virtue sent a tame low effort bobbling straight at Hamilton before the Seasiders survived a couple of scares at the other end thanks to some desperate last-ditch blocks.
Dundee almost doubled their lead with the last action of the game as Josh Mulligan's shot was charged down after Myles Boney's poor clearance.
Blackpool are next in action at AFC Fylde next Tuesday.
First half XI: Mafoumbi, Feeney, Nottingham, Tilt, Shaw, Spearing, Thompson, Devitt, Kaikai, Delfouneso, Gnanduillet
Second half XI: Mafoumbi (Boney), Turton, Edwards, Anderton, Bola, Virtue, Guy, Pritchard, Tollitt, Ceesay (Roache), Yussuf
Attendance: 2,405 (140 Blackpool)