Reading 3 Hull City 1
But an acrobatic strike form Kevin Doyle was quickly followed by Glen Little's side-foot finish to seal a 3-1 win for Reading and extend their club record unbeaten run to 21 games.
It was a deserved win for Steve Coppell's Royals but only after Hull had weathered an early storm to threaten an upset.
Convey's seventh minute strike looked set to open the floodgates such was Reading's early dominance.
The American international winger had already threatened with a volley which was tipped over by Boaz Myhill and from the resultant corner Ibrahim Sonko saw a header nodded off the line by Barmby.
A swift attacking move saw the Royals take the lead a few minutes later when Graeme Murty won the ball and fed Doyle whose inch-perfect pass allowed Convey to beat the offside trap and coolly drive beyond Myhill
The Hull keeper then stopped a side-foot effort and a week Ivar Ingimarsson strike either side of a superb finger-tip save at full stretch to deflect a Leroy Lita shot around his post.
And while Myhill was keeping his side in the match there was always a chance of Hull rocking the Reading boat.
Ben Burgess was denied by a fine reflex save by Marcus Hahnemann who then produced a point-blank save to deny Leon Cort and then keep out the rebound from Burgess.
When Hahnemann was finally beaten by a looping Barmby header the post came to Reading's rescue.
Encouraged by those chances, Hull continued to attempt to stem the flow of Reading attacks and catch the promotion chasing side of the counter attack.
And they were level 11 minutes into the second half when full-back Mark Lynch broke clear down the right and crossed for Burgess to nod down and Barmby headed home from close range.
After that it appeared Peter Taylor's side might frustrate Reading but the home side broke through again on 69 minutes when Little knocked down Convey's corner for Doyle to scissor-kick an effort beyond Myhill and in off the underside of the bar.
Seconds later, Hull were finished off by Little who fed Convey than ran on to the return pass to strike home his fourth goal of the season.