After dominating the game without reward, the Royals found themselves behind the eight ball midway through the second half when Zurab Khizanishvili was sent off.
However, the Tykes failed to make use of their advantage as Kebe capped a sensational individual performance with a 78th-minute goal, before Ian Harte and Hal Robson-Kanu topped the result off with late strikes.
Going into the game desperate for three points to kick-start their season, Reading did much of the early running with Jobi McAnuff looking particularly threatening.
The former Wimbledon and Crystal Palace winger played in a wonderful ball to Simon Church, which the striker just failed to convert, before seeing his fizzing shot blocked by Jason Shackell.
They should have got the reward their endeavour deserved in the 16th minute, but Church headed just wide after an excellent cross from Kebe. The striker had an even better chance moments later, only to see his glancing header saved by Luke Steele.
If McAnuff was impressive, it paled in comparison to Kebe, who was in truly irresistible form, nearly forcing Stephen Foster into an own goal.
Barnsley started to get a foothold in the game midway through the half, although their neat passing failed to fashion opportunities.
Brian McDermott's troops, meanwhile, remained as dangerous as ever going forward, Matt Mills hitting just over the crossbar from six yards after Harte's corner.
Reading picked up where they left off at the start of the second half, but continued to find an opener increasingly elusive.
The Tykes were showing glimpses of the danger they posed, though, as Chris Wood forced a good save from Adam Federici .
And the visitors' cause was helped moments later when Khizanishvili, on loan from Blackburn, was sent off for a bookable offence - both of which were controversial - much to the dismay of the home support.
If anything, the decision seemed to have a galvanising effect on the Royals who continued to push forward in numbers despite their disadvantage.
As the game wore on, Barnsley's one-man advantage began to take its toll and they started to fashion opportunities, Adam Hammill forcing a save from Federici courtesy of a long-range effort, before Diego Arismendi headed just wide.
The tricky Kebe continued to cause all sorts of problems, though, bamboozling the Tykes' backline en route to putting in a great cross which Robson-Kanu could not direct goalwards.
Kebe got his just rewards moments later, capitalising on McAnuff's excellent left-wing cross to get in front of the defender and beat Steele with a bullet header.
McAnuff nearly made it 2-0 moments later through a deflected free-kick, but it went inches wide.
However, they did get a second when, after Nathan Doyle brought down Kebe on the edge of the area, Harte fired home the resulting 20-yard free-kick, before Robson-Kanu added gloss to the scoreline in injury time.