On-loan Preston defender Eddie Nolan had broken the deadlock in a must-win game for the Sheffield side before Tom Cleverley levelled matters with a spectacular free kick.
Varney grabbed the points with an angled strike from 18 yards to leave Wednesday four points clear of third from bottom Crystal Palace.
Wednesday carved out the better chances in a scrappy affair with James O'Connor going close with a long range strike which had Scott Loach scrambling across his line as the ball dropped the wrong side of the woodwork.
The Watford keeper foiled Wednesday by pulling off an eye0catching stop to turn Darren Potter's free0kick against the woodwork, before Tommy Spurr foiled Will Hoskins with a last-ditch challenge as Watford caught the Sheffield side on the break.
Nolan grabbed the opener in the 55th minute after running onto Darren Potter's pass and rounding two defenders before cutting inside and drilling a low strike from 15 yards beyond Loach's reach.
Cleverley levelled matters in the 67th minute after Wednesday conceded a free-kick on the edge of the area.
He curled the ball into the top right-hand corner beyond the reach of Lee Grant.
Wednesday endured some nerve racking minutes as Watford, who ran out 4-1 winners when the sides met at Vicarage Road in October, forced the pressure.
But it was Wednesday who had the last word when on-loan Derby striker Varney slammed the ball past the helpless Loach from 18 yards.