Steven Defour laid on both goals with Hendrick heading home his corner in the 38th minute and Keane rising to nod in the winger's left wing cross five minutes into the second half.
Belgian international Defour was man of the match with Keane and manager Sean Dyche saying he gave Burnley extra quality.
"He's played brilliantly ever since he came into the team, you can see the quality he's got," said Keane.
Dyche, a former Watford player and manager, said Burnley had worked hard to sign Defour, who is closing in on 50 caps, for a club record 8 million pounds ($10.38 million)in August.
"His quality rubs off on others, he's got a bit more of an assured manner in possession," said Dyche.
Watford were aiming for a third straight league win but could not find the form that helped them comfortably beat Manchester United 3-1 and West Ham United 4-2.
Burnley defended well, in contrast to Watford's poor marking at set pieces, and kept Etienne Capoue and captain Troy Deeney, who forced a fine point-blank save from Heaton, in check.
"We got bullied to a man all over the pitch," a disappointed Deeney said. "Burnley set up and we couldn’t handle it.
"We played so well against Manchester United recently but it never really looked like it was going to happen."
($1 = 0.7710 pounds)
(Reporting by Rex Gowar; Editing by Ken Ferris)
