Danny Graham had put the visitors ahead before Bates failed to spot an obvious handball from Mike Williamson, which denied Robert Earnshaw a clear run on goal and could have seen the defender red-carded.
Forest equalised through Dexter Blackstock in the first half but Williamson popped up to fire Watford back into the lead, before Smith made sure of three points.
A late strike from Dele Adebola gave Forest brief hope, before Tom Cleverley struck in injury time for Watford.
A lacklustre first ten minutes was followed by an action packed first half that ultimately left both sides to wonder how they had only netted once.
Dexter Blackstock had flashed a shot high over the bar for Forest after good work from Nathan Tyson, while Ross Jenkins planted a header high of the target with the goal at his mercy for Watford.
Scott Loach had to produce a smart save to swat away a firm Robert Earnshaw header, before Forest lost midfielder Lewis McGugan to a head injury after he had bravely challenged the keeper for a high aerial ball.
The injury seemed to halt Forest's growing momentum and, within five minutes, Watford had taken the lead.
Tommy Smith's trickery had both Chris Cohen and Joel Lynch on the back foot and the Hornets' danger man lifted a clever cross to the far post, where Graham headed home from close range.
Watford had a remarkable escape when last man Mike Williamson obviously stuck out a hand to halt the flight of the ball and prevented Earnshaw racing clean through on goal, with referee Tony Bates provoking the City Ground into a rage by waving play-on.
But Forest's equaliser came five minutes later as McKenna's clever ball picked out Blackstock's rampaging run through the middle, with the striker controlling on his chest before bundling home from close range.
Forest could have had a second before the break as Earnshaw angled a powerful shot into the side netting.
Watford began the second half brightly with both Scott Severin and new signing Tom Cleverley firing wide when they should have done better.
Williamson did then pounce, controversially, to put Watford ahead again, after Smith's shot had rebounded back kindly off the post.
Smith then lashed home a spectacular finish from 30 yards to make it 3-1, before substitute Adebola gave Forest fruitless hope.