Pavel Pogrebnyak had nodded Brian McDermott's men into a shock early lead, but from that point on the game was bossed by the hosts, who were swiftly back on terms thanks to Michael Dawson before taking the lead through Adebayor's excellent header early in the second half.
Andre Villas-Boas will be concerned by the fact that his side failed to put the game to bed earlier despite their clear superiority, with Reading close to snatching a leveller in the second period before substitute Clint Dempsey's deflected effort made the game safe 11 minutes from time.
Reading made a dream start as they took the lead with only four minutes on the clock when Ian Harte's superb free-kick from outside the box crashed off the crossbar with Hugo Lloris well beaten and Pogrebnyak reacted first to nod home into an empty net.
Spurs were stung and Adebayor nodded wide at the far post from the excellent Aaron Lennon's cross, before they restored parity almost immediately as skipper Dawson got ahead of Royals striker Pogrebnyak at the near post to glance home Gylfi Sigurdsson's corner from the left.
The first half continued with consistent pressure from Spurs, but they were unable to find a way past the impressive Adam Federici in the Royals goal, with many of their attempts coming from range, typified by a blistering long-range drive from Mousa Dembele which was narrowly wide as he burst clear despite his shirt being pulled by Jem Karacan.
Jermain Defoe then turned Mikele Leigertwood inside and out before firing in a powerful shot which whistled inches past the post, with the England striker going close again as half-time approached, but his second shot from outside the box lacked power and was gathered by Federici, who had to be alert moments later to gather another effort from distance by Dembele at the second attempt.
Jobi McAnuff blazed over the bar on a very rare foray forward for Reading before Federici was called into action once again, plunging low to his left to turn away a deflected effort from Sandro which clipped Sigurdsson on its way towards the goal.
The second half commenced in the same manner with which the first ended, Federici diving away to his left to comfortably gather a curling effort from Defoe, but the Royals keeper was powerless to keep out a towering header from Adebayor after Lennon took on Harte and clipped over a delightful cross in the 51st minute.
Reading were offering nothing as an attacking threat and Spurs nearly made it 3-1 when Lennon burst clear and saw his initial shot blocked before being fed by Adebayor, only for Alex Pearce to make a vital interception. The winger was at the centre of yet another attack with the game into its final third, cutting a low cross into the area which Defoe could only fire wide, with Sigurdsson well-placed behind the striker.
Spurs were almost made to pay for their profligacy in front of goal as Pogrebnyak burst into the area and forced Lloris to forego his role of virtual spectator with a low save with the Royals forward then heading the follow-up narrowly wide of the target.
Jimmy Kebe was also inches away from levelling in the 75th minute, only to be denied by an excellent last-ditch tackle from Kyle Walker, with Pearce's header from the resulting corner heading towards goal only to be unwittingly deflected wide by Pogrebnyak with Dawson and Lloris in close attendance.
The increasing nerves among the home supporters were eased in the 79th minute when substitute Dempsey, who had only been on the field for four minutes, struck a shot from outside the box which took a wicked deflection off the leg of Leigertwood and looped over the unfortunate Federici, who reserved his best save for last as he tipped away Scott Parker pile-driver.