Cleverley and Lansbury provided athleticism and intelligence off the lone striker Danny Graham and left Wednesday overrun in the middle of the park.
Defender Adrian Mariappa gave Watford the lead from close range before Lansbury swept in a fine second after a one-two with Cleverley.
Marcus Tudgay gave Brian Laws' side some hope with a response but Jon Harley and then Lansbury again scored excellent second-half goals to give the Hornets a thoroughly deserved three points.
Wednesday could have gone ahead through Luke Varney in a lively opening before Watford captain Mariappa gave them a 21st-minute lead.
Cleverley's corner found its way through to substitute John Eustace, and when he shanked a shot across the face of goal Mariappa was perfectly placed to steer in from six yards.
If there was an element of fortune about their opener, Mackay's side crafted a superb second five minutes later.
Lansbury picked up on a poor clearance and played the ball into Cleverley's feet on the edge of the area.
Cleverley played a reverse pass back into his stride and despite two defenders converging on him, Lansbury glided through the pair with a deft touch and buried a low shot under the body of goalkeeper Lee Grant.
Cleverley then saw a powerful header well held by Grant as Watford looked dominant, but the hosts managed to concede a poor goal in stoppage time.
Tommy Spurr hurled in a long throw from the left and when England Under-21 goalkeeper Scott Loach stayed on his line Tudgay rose to thump a header down into the bottom corner.
It was a lifeline for Laws, and the Wednesday boss introduced Tommy Miller at the break in a bid to win back control of midfield.
But Lansbury and Cleverley continued to find space in between the Owls lines and the two of them combined for Harley to make it 3-1 in the 54th minute.
Cleverley's corner was again not cleared and after Lansbury had beaten Miller to the loose ball he picked out Harley in space inside the penalty area.
The former Chelsea man took a touch and drove an unerring strike past Grant and into the top corner.
Harley then crossed for Lloyd Doyley to head narrowly wide before Lansbury grabbed his second in the 61st minute.
Again Cleverley was the architect, dancing around three desperate challenges as he surged into the penalty area before cutting the ball back for Lansbury to drill home from six yards.
That was game over and the sides played out the last half-hour with little fanfare as the Owls were left to reflect on a miserable evening.