The striker, who scored a 93rd minute winner against Bohs at Dalymount Park last April, repeated the feat in a dramatic finale to sink Harps who find themselves in real trouble at the bottom of the table.
It was his fourth goal of the season and arguably his most important as it took Derry above Dundalk into second place.
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Derry had dominated the ball in the opening stages but it was Harps who broke the deadlock when new signing, Rob Jones powered in a header from a corner on 31 minutes.
Derry huffed and puffed and it wasn't until the introduction of recent signing Ryan Graydon from the bench they began to find a way in behind the resolute Harps defence.
And the Dubliner headed Derry back into the game with 11 minutes left on the clock after Cameron Dummigan found him with a long ball over the top.
With SEVEN minutes of stoppage time signalled Will Patching found Akintunde at the back post from a free-kick and the striker headed into the net before racing towards the travelling support.
Ruaidhri Higgins made three changes from the team which lost to Riga on Thursday night. Matty Smith, who was suspended for the trip to Latvia, returned to the team at the expense of Brandon Kavanagh who dropped to the bench.
Bolton-bound Eoin Toal scored a dramatic late equaliser when the teams met last at Brandywell in a 2-2 draw, however, he was omitted from the matchday squad for this visit to Co. Donegal.
The City skipper picked up an ankle injury in Riga and was replaced by Ciaran Coll who made his sixth start of the season.
The Candy Stripes' top scorer Jamie McGonigle was also back in the starting XI, replacing James Akintunde who started on the bench.
New signing Sadou Diallo was also on the bench but Michael Duffy, who made his comeback from a broken leg for the final 15 minutes of Thursday night's European clash was a notable absentee with unconfirmed reports he sustained a hip flexor injury.
The winger watched from the stands alongside the injured Ciaron Harkin and Ronan Boyce.
Harps also made three changes with goalkeeper Mark Anthony McGinley returning in place of Gavin Mulreany.
Filip Mihaljevic, who also scored in the last meeting between the two sides at Brandywell, dropped to the bench with Conor Tourish back in the starting line-up alongside debutante Harry Nicolson.
Patching, who has scored four times against Harps for Derry, found himself in a great position inside the opposition penalty area after Dummigan found Lafferty with a superb crossfield ball.
The midfielder slotted the ball through the legs of his marker but he was off balance when attempting the shot at goal and skied it high and wide on six minutes.
Derry were controlling possession for the opening 20 minutes with Harps only danger coming from long throw-ins from Ethan Boyle on the right which created a few nervy moments for the visitors inside a crowded penalty area.
The Candystripes were applying the pressure without troubling McGinley and Smith's low strike from an angle on 25 minutes went narrowly wide of the post.
For all of Derry's possession, it was Harps who broke the deadlock. Not surprisingly it came from a set-piece on 31 minutes as Donelon swung the ball in dangerously and Jones peeled off his man before steering his header powerfully beyond Brian Maher.
It was a terrific header from 10 yards from the Scotsman and a real blow to City who will have had flashbacks from Riga where they dominated the opening half hour before conceding the opening goal from the opposition's first opportunity.
Smith was fouled on the edge of the Harps penalty area with several Derry players claiming the contact was inside the box on 38 minutes.
It was an early opportunity to level the game with the ball placed at the feet of Patching who scored from a stunning free-kick on his last visit to Ballybofey in a 2-1 win.
This time the Englishman just didn't have the accuracy as he curled it over the wall and harmlessly over the bar.
Harps, who registered just one win in their previous 10 games, took that slender lead into the break. Derry created little chances of note in that opening 45 minutes and needed a big reaction in the second half if they were to leapfrog Dundalk into second place.
Higgins made a double substitution at the start of the second half with Diallo coming on for his debut to replace Joe Thomson. Kavanagh replaced Danny Lafferty with Dummigan slotting in at right back.
It was a third Derry sub, winger Ryan Graydon who found himself with a glorious chance for his first goal for the club when Patching lobbed his free-kick towards the back post but the City newboy's downward header bounced over the bar just moments after coming on.
Harp boss Ollie Horgan made a triple change with Bastien Hery, Mihaljevic and Mark Timlin entering the fray.
Derry looked more menacing going forward with the pace of Graydon on the left but Harps defended resolutely.
Amazingly Derry's first shot on target arrived on 74 minutes as McEleney's 25 yards strike needed to be tipped over the bar by McGinley.
Four minutes later Patching found the run of Graydon on the left side and he made his way into the box before cutting it back to the supporting Diallo but his shot was charged down by Tourish.
Finally Derry broke Harps resolve on 79 minutes when Dummigan found the run of Graydon with a ball over the top. The winger held off Boyle and as McGinley raced to gather the ball Graydon got his head to it and it bounced into the empty net.
Derry were pushing for a second and McEleney left three Harps defenders on their backsides with a lovely feint 20 yards from goal. He cut back onto his right foot but his strike sailed over the crossbar.
The fourth official signalled seven minutes of additional time and there was to be late, late drama.
In the third minute of stoppage time Patching swung a free-kick towards the back post where Akintunde rose to head the ball home.
Finn Harps: M. McGinley: E. Boyle, H. Nicolson (D. Duncan 93), R. Slevin, C. Tourish, R. Donelon (B. Hery 62); B. McNamee (M. Timlin 62), E. Nzeyi, R. Connolly (Mihaljevic 63), R. Rainey (S. O'Donnell 93); R. Jones; Subs Not Used - G. Mulreany, L. Rudden, A. McCaffrey, J. Carrillo, L. McGing.
Derry City: B. Maher; J. Thomson (B. Kavanagh h-t), S. McEleney, C. McJannet, C. Coll; M. Smith (R. Graydon 60), C. Dummigan, P. McEleney, D. Lafferty (S. Diallo h-t); W. Patching; J. McGonigle (Akintunde 78); Subs Not Used - N. Gartside, E. McLaughlin, J. Malone, C. Porter, D. McCallion.
Referee - Derek Tomney.