Promotion favourites Boro went into the game without a single goal on their travels in the league this season and they went behind after only 17 second when David Wheater's poor passback gave former Boro trainee Graham a simple chance which he took with aplomb.
Ten minutes later it got worse for the visitors when they failed to clear from a corner and Jordon Mutch sent in a half-volley which gave Jason Steele no chance.
Graham spent four years at the Riverside Stadium before being released and he showed Boro what they were missing when he got on the end of Don Cowie's cut-back for his second and Watford's third after just 20 minutes.
Middlesbrough tried to find a way back into the match and Scott Loach denied Gary O'Neil before an own goal from Adrian Mariappa gave them faint hope with 10 minutes remaining.
However, Watford held on for the three points - much to the frustration of the travelling Middlesbrough faithful.
Buoyed by their stunning 6-1 win at Millwall last week, Watford came flying out the traps and were in front within a minute.
Wheater's attempted backpass was woefully short and Graham nipped in before rounding Steele and rolling the ball into the net.
To their credit Middlesbrough responded well to the early setback and Leroy Lita had a good chance to draw them level but his shot was tipped round the post by Loach.
Watford duly capitalised and two minutes later Cowie's corner was cleared into the path of Mutch who slammed home a superb half-volley from 25 yards.
Middlesbrough were looking shaky at the back and the visitors' defence switched off from a short corner allowing Mariappa to get in a header that went just over the bar.
With 20 minutes gone Watford made it 3-0 when Cowie got past his marker on the left and drove to the by-line before squaring the ball for Graham who made no mistake from close range.
Jeers rang out among the Boro fans who had made the long journey south and their team showed little sign of coming back into the match before the break.
Strachan's side showed more purpose at the start of the second half and almost got a goal back when O'Neil was left unmarked at the far post from Barry Robson's cross but Loach made a superb smothering save.
However, Watford still looked dangerous whenever they had the ball and Marvin Sordell got in one-on-one with Steele but was denied by a superb last-gasp challenge from Tony McMahon.
With 10 minutes remaining Scott McDonald's shot was saved by Loach and Mariappa headed the loose ball into his own net but it only proved to be a consolation.