Fifth time lucky as Ware pick up three points for the first time.
Bishop and Asamoah strikes go unanswered to end a barren spell for the Blues.
When Nana Asamoah ran to high-five supporters in the disappointingly sparse crowd four minutes into added time at the end of this game it was in relief after he had just scored Ware's second goal. A first victory was assured and the monkey on Ware's back had been removed.
That said there was little else for the Blues to take from a dour struggle. Ware have played much better than this and lost. Maybe it was the heat that reduced both sides to some pretty ordinary football. It couldn't have been the pitch which was in excellent condition and really didn't get the response from the players it deserved.
Ware did have their moments though with a cross from Paul Cooper deserving more than it got, Kieran Bishop inches from making contact with another cross with just the 'keeper to beat and Khale Dacosta blasting high and wide from inside the six yard area.
In the second half Anthony Thomas was on the end of yet another cross and, having missed a chance in the first period, connected this time but put his header just inches over the bar. That was the signal for Rod Young to come on in a bid to liven up the front runners, he played well but it was a day when nothing seemed to gel for the team.
That said DaCosta set up Murat Karagul three minutes after the substitution but the midfielder hit the excellent opportunity wide and it seemed that Ware were destined to play out a draw.
But fortune smiled on them after 68 minutes when Ricardo Diniz in the home goal failed to deal properly with a high ball and it fell beyond him at the feet of Kieran Bishop. It was an open goal and even in this season of missed chances wasn't going to be spurned by last campaign's top scorer.
United upped their tempo after this but could only get the better of the Ware defence once when a close range effort was sent over the bar. Tempers became unnecessarily frayed in the closing minutes and the referee produced a number of yellow cards as both teams sweated to find or prevent a break through. In the end Asamoah sealed it with a shot from the left that eluded Diniz's hand and found the bottom of the net.
Goals aside no player made a real impact in this dour struggle though Ben Crilley's calmness in defence caught the eye.
There's a good piece about the game on the Greenford website here.
Ware: Jack Smith; Jack Fowler, Alaa Oujdi, Jamie Smith (Nana Asamoah 60 mins), Ben Crilley, Ajet Shehu, Paul Cooper, Murat Karagul (Kazim Bishop 83 mins), Kieran Bishop, Khale Dacosta, Anthony Thomas (Rod Young 52 mins). Unused subs: Charlie Ledula, Danny Charles.