The Exiles controlled long periods of the game with fly-half Barry Everitt slotting four penalties for the hosts, but they failed to create any try-scoring opportunities, barring the final five minutes of the game with Leeds digging their heels in.
Leeds lost England fullback Iain Balshaw ahead of the match and the visitors could have done with his finishing abilities in a dis-jointed first-half that saw the Exiles leading before the break, before Hyde slid over in the 40th minute after chasing down a loose ball.
Fly-half Gordon Ross converted to extend the lead with Tykes ending the first half on top.
Ross pushed his team further in front with a penalty after the break with Everitt responding with his third of the match.
But the Leeds No.10 pushed Tykes 16-9 ahead with a drop-goal, only for Everitt to set up what should have been a frantic finale when his 68th-minute penalty pulled the hosts within four points.
Everitt's handling, however, let him down and brought to a halt one promising attack and the Exiles were grateful to see David Rees lose control of the ball near the line after Michael Horak's error at the back.
But the game reached a crescendo in the final moments with the hosts camped on the Leeds line.
Hyde was sin-binned by referee Sean Davey for killing one attack, but the Tykes withstood a barrage of drives at the line from Phil Murphy until the Exiles lost the ball in their final effort
For Leeds:Pens: Everitt 4
For London Irish:Try: HydePens: Ross 2DG: Ross