The Turkey international pounced on 20 minutes after David James had kept out a volley from former Pompey favourite Gary O'Neil on his return to the south coast.
Portsmouth have now gone 540 minutes without a goal at home and showed little to suggest this embarrassing statistic will be changed any time soon.
In a dull and dreary opening of little consequence with both teams appearing weary from the busy Christmas period, Niko Kranjcar struck the first shot on target as Lauren's deflected cross found the Croatian in space on the edge of the penalty area.
The tedium was showing few signs of lifting until Boro took the lead on 20 minutes after O'Neil's free-kick from the far touchline was only half-cleared.
Stewart Downing popped up on the right-hand side of midfield to swing in a well-flighted centre for Lauren to get his bearings hopelessly wrong and O'Neil promptly volleyed towards goal.
James managed to get a hand to take the sting out of the shot, but Tuncay was free to tap into the unguarded net from close range for his fourth goal of the season.
With a virtually silent Fratton Park crowd doing little to spur their side on, Pompey attempted to hit back and went close through Papa Bouba Diop from long-range.
That was not without a further scare for the home side as Lauren was caught napping trying to play offside, allowing Downing to expose his lack of concentration.
The England winger progressed down the touchline and teed up Tuncay, but he mis-kicked and Dong-Gook Lee then further failed with a second attempt.
Minutes before the break and Pompey spurned a decent opportunity to draw level when Benjani Mwaruwari crossed back into a crowded penalty area only for Diop to arrive late and spoon over from just eight yards out.
The second half proved far more frenetic than the pedestrian nature of the first as O'Neil teed up Lee only for the Boro striker to have his first effort blocked on the line by Lauren and then saved on the second occasion by James.
Portsmouth tried as they might to carve an equaliser but it was a desperately off day for the home side as they resorted to throwing long balls into the area which were calmly dealt with by the rock-solid Jonathan Woodgate and Robert Huth.
Nwankwo Kanu did strike a post from close range after a goalmouth scramble, but it was far more than Pompey deserved as it proved an extremely bad day at the office for Harry Redknapp's side.