Watford boss Malky Mackay signed a new three-and-a-half year deal this week and he celebrated that with a victory after a fine individual goal from his star player.
Kenny Jackett’s visitors had arguably the best of a tight game but could not find a response to the prolific Graham’s finish early in the second period.
The win edged Watford ahead of Millwall in the table but both sides look destined to end the season marooned in midtable.
Millwall midfielder Liam Trotter turned sharply to send a low shot wide in a lively start before Hornets winger Don Cowie went close with a speculative drive from fully 25 yards which dipped just over the top.
The Lions looked dangerous on the counter-attack and Danny Schofield should have tested Watford keeper Scott Loach on the quarter hour mark at the end of one break but fired over.
Cowie’s free-kick was then headed over by Troy Deeney as the sides continued to trade chances and a decent move saw on-loan Aston Villa forward Andreas Weimann drill a low effort past the post as the poor finishing continued.
Millwall goalkeeper David Forde was finally involved in the final minute of the half when he had to tip a rocket from centre-half Adrian Mariappa over the top as it threatened to creep into the top corner.
Loach was called into action at the start of the second half when he got down well to keep out a shot from James Henry, before the hosts took the lead in the 51st minute.
Cowie’s ball from the left found Graham on the edge of the area and the former Middlesbrough man pulled off a superb turn and shot which beat Forde at his near post and found the bottom corner.
Jackett’s reaction was to make a double change with Kevin Lisbie and Scott Barron coming on as Millwall looked for a leveller.
Alan Dunne headed straight at Loach before the home side wasted two good chances to kill the game off on the break.
Winger Will Buckley was the first culprit as he broke clear before dragging his effort wide, before substitute Marvin Sordell cracked in a half-volley which was well blocked by the body of Forde.
Millwall striker Steve Morison had endured a frustrating afternoon and spurned his only opportunity of the game with 16 minutes left.
Lisbie was energetic to make ground down the right and he was able to pick out Morison breaking into the area, but the forward shot wide of the mark.