Cotterill spent £1.5million to bring Huseklepp to the south coast from Bari before quitting Pompey to take over at Nottingham Forest last month.
And the Norwegian winger repaid a chunk of the fee on Saturday by scoring two goals and setting up Dave Kitson for the other as Portsmouth leapfrogged their visitors in the Championship.
Pompey expect to appoint Cotterill's successor during the international break, with West Brom assistant Michael Appleton the latest name in the frame.
But caretaker duo Guy Whittingham and Stuart Gray were able to sign off with a win thanks to Huseklepp's brace and Kitson's header.
Yet it was hard luck on Forest, who dominated for long periods only to be floored by sucker punches late on in both halves.
Most of the early opportunities they created fell to Lewis McGugan, who curled a fourth-minute free-kick wide, dragged another shot the wrong side of the post and then miscontrolled Chris Gunter's pass right in front of goal, allowing Pompey goalkeeper Stephen Henderson to smother the ball.
Robbie Findley also fired a good chance wide from the edge of the area after Manchester City loanee Abdul Razak gave possession away, and Wes Morgan's header was too close to Henderson.
Eight minutes before the break McGugan tried his luck again with a 30-yard free-kick, but Henderson was able to tip it over the crossbar.
Pompey had been restricted to long-range efforts, with Kitson's shot deflected wide and David Norris' drive sailing over the top.
But when Hayden Mullins took aim from 25 yards a minute before the interval, the ball crashed off the crossbar and fell to Huseklepp, who expertly curled the rebound past Forest goalkeeper Lee Camp and into the top corner.
After the break it was Pompey who took the early initiative with Camp denying Varney and Kitson heading over the bar.
But they had a let-off at the other end when Luke Chambers met McGugan's corner and his header was hacked off the line by Mullins.
And the hosts were indebted to Henderson for denying Findley on the hour.
Marcus Tudgay's cross was controlled superbly the striker, who turned sharply and fired at goal only for Henderson to make a fine reaction save.
Gunter also squandered the chance to equalise when he volleyed over, and instead Pompey doubled their lead when Kitson nodded in Huseklepp's corner in the 77th minute.
And Cotterill's misery was complete six minutes from time when David Norris teed up Huseklepp to prod in number three.