Fulham 1 Portsmouth 0
Avram Grant's visitors were the better side for long periods of this uninspiring match but, as has been the case for much of the season, they only had themselves to blame for not taking their chances before giving a sloppy goal away.
And on this occasion it was left-back Nadir Belhadj who should hold his head in his hands as Damien Duff robbed him of possession inside his own area and laid the ball across goal to Greening to score his first ever goal for the club at the back post.
The result ensured Roy Hodgson's hosts ended their own terrible run of seven league games without a victory but, while they can look forward to the rest of their season from the safety of mid-table, Portsmouth are surely doomed.
Labouring under financial chaos for the entire season, Grant saw his two most valuable assets, Younes Kaboul and Asmir Begovic, sold from under his nose on transfer deadline day, with the money from those sales ensuring the players and staff received their wages only a day late this month.
Yet their side has been left woefully short of depth as a result, although the Israeli was still able to field eight full internationals in his starting line-up.
And it was the visitors who dominated the opening stages with their front three of Aruna Dindane, Frederic Piquionne and, in particular, Kevin-Price Boateng causing havoc.
However, chances were at a premium with only Piquionne testing Fulham keeper Mark Schwarzer having cut in from the left after ten minutes.
Fulham's fans were growing increasingly frustrated at their side's poor display, yet they missed an astonishing chance to take the lead just after the half-hour mark as debutant Stefano Okaka - who has joined on loan from Roma for the rest of the season - wasted a wonderful opportunity.
It seemed all the Italian had to do was make contact with the ball as Greening's knock-down found him lurking just one yard from goal but somehow Okaka put it wide.
Yet while Okaka's miss was at least something to talk about, the second half failed dreadfully to live up to expectations which, as Fulham were in the middle of an horrendous injury crisis, were relatively low.
The game developed into a gritty midfield battle with either a moment of genius or a shocking mistake likely to settle game.
So it proved as Belhadj, playing for the first time since returning from Africa Cup of Nations duty, dwelt on the ball and allowed Duff in.
There was still a lot to do but the Republic of Ireland international picked out former West Brom skipper Greening at the far post to slide home the goal that lifts Fulham to 10th and leaves Portsmouth an ominous six points from safety.