Grzegorz Rasiak combined with fellow former Hornet Jobi McAnuff to smash home an early opener for Reading but Graham took advantage of some slack defending to level for Watford and leave Rodgers still waiting to end the wait for a home victory.
The Royals have now incredibly gone 14 home games without a win since beating Wolves in January and not even the late
sending-off of Watford striker Nathan Ellington could help.
Reading captain Ivar Ingimarsson returned to make his first appearance since injuring his knee in January while McAnuff made his debut against the club he signed from last month.
McAnuff was given a torrid reception by the away fans but made a chance in the third minute after some fine wing play.
He cut a ball back into the area where Rasiak - who was on loan at Watford under Rodgers last season - saw his header saved by Scott Loach and Gylfi Sigurdsson grazed the post with the rebound.
It was a close call for the visitors but the Royals did go ahead in the seventh minute.
Again McAnuff beat his man all too easily and crossed for Rasiak to smash into the top corner from 10 yards with his left foot.
It was only the fifth goal Reading have managed at home since that Wolves win eight months ago and the relief was palpable.
The Poland international was proving too much to handle for his former team-mates and again tested Loach before heading another opportunity onto the roof of the net.
Watford striker Graham skidded a shot narrowly wide from the edge of the area as Malky Mackay's side pushed forward but Royals midfielder Brian Howard then came close to a second with a long-range drive which Loach held.
The visitors came within inches of an equaliser at the start of the second half after a long throw was not cleared.
Henri Lansbury struck a shot from the edge of the area which took a deflection and looked destined for the top corner.
However goalkeeper Adam Federici managed to somehow tip the ball onto the crossbar and the defence scrambled the ball away.
Watford were much improved from the opening period and deservedly drew level in the 66th minute after an error from Federici.
A harmless looking ball was played forward but Federici and defender Darren O'Dea left it for each other and Graham nipped in to steal an easy goal.
Ellington came on as a late substitute and, after being booked for preventing a free-kick from being taken quickly, saw a second yellow card in the 88th minute for a foul on Jem Karacan.