A gritty and determined second half performance from Ulster saw them win their first PRO12 game of the season in Galway.
Traililng 7-5 at the interval, Ulster rallied in the second half to deservedly take the victory which hauled them off the bottom of the table.
Connacht took the lead on 10 minutes when after a surge by winger Fionn Carr and then a break by Matt Healy was halted inches short, further recycled ball led to outhalf Dan Parks skipping through the smallest of gaps for the opening try. Parks added the extras for a 7-0 lead.
Ulster did fight back at once and after a break from No 8 Nick Williams, fullback Jared Payne was stopped five metres out.
At the next phase Paddy Jackson side-stepped his way through, but was held and then Luke Marshall was held up short.
But when Ulster got the ball again, winger Michael Allen went in for the try. Jackson failed to convert the touchline conversion after 14 minutes.
Connacht dominated following that and will have been disappointed not to have only been two points ahead.
Parks missed a penalty opportunity on 28 minutes and two minutes later, after what had been a rare sortie from Ulster into opposition territory, Jackson failled with a penalty chance on 31 minutes.
Ulster finished the half strongly, Ricky Lutton came on as a replacement for the injured Declan Fitzpatrick and made an immediate impact in the scrum.
Jackson’s penalty to touch saw ball moved to the right and a drive by Henderson looked promising, only for the second row to drop ther ball.
Ulster dominated in the second half and finally went in front through a Jackson converted try after the outhalf had kicked a penalty.
Just after the hour mark Jackson scored a vital penalty to make it 18-7 and put distance between the sides.
Connacht rallied in the closing minutes, but were held up twice on the line as the Ulster rearguard dug in bravely.