Fletcher was brilliant as he grabbed a super header in the first half and a 25-yard strike after the break to show what an emerging talent he is.
Hibs fans were forced to wait for the return of their hero, Riordan, as a niggling injury kept him on the bench.
But Riordan's absence made little difference as Hibs started strongly. Dean Shiels' throughball sent Colin Nish through the middle but his attempted cut-back was behind Fletcher.
Fletcher came close after eight minutes, climbing above Danny Grainger but heading over the bar from Shiels' tantalising cross.
But Fletcher made no mistake after 22 minutes when Colin Nish turned Ian Murray's cross into the danger area. The Scotland striker stooped to send a great header into the roof of the net from ten yards and Hibs were in front.
But United came back strongly and Francisco Sandaza got between Chris Hogg and Rob Jones to fire a 20-yard effort narrowly over.
And when Jones and Yves Ma Kalambay left a long throughball to each other, Sandaza missed a glorious chance to equalise as he dragged his shot across goal and wide of the target.
But the visitors did go in level at the break thanks to a stunning goal from skipper Lee Wilkie in first-half stoppage time. His first effort was blocked by Jones but, as the ball broke back to him 20 yards out, he hammered a great right-foot shot into the bottom corner of the net.
There was still no sign of Riordan at the start of the second half and it was Sandaza who continued to catch the eye with a dazzling run along the byline that was halted by Jones' tackle.
And United continued to threaten as Jon Daly got on the end of Grainger's cross to force a save from Ma Kalambay.
Hibs replied with long-range efforts from Shiels and then Nish but neither troubled Lukasz Zaluska.
Riordan entered the action to a rapturous welcome from the Hibs fans after 61 minutes and watched as Ma Kalambay made a brilliant save low to his right to deny Sandaza.
But in the 63rd minute Hibs were back in front after a glorious move involving Shiels and Nish which Fletcher finished brilliantly from 25 yards with a first-time effort.
The home side were reduced to ten men after 68 minutes with Sol Bamba red-carded on his debut for a second booking after two late tackles on Scott Robertson.
And it took another fine save from Ma Kalambay to keep Hibs in front as he beat away a 20-yarder from Craig Conway.
But Hibs' ten men hung on to record a vital win that they scarcely deserved.