Eustace hit the only goal in a poor game which leaves Malky Mackay's men five points behind the top six with nine points to play for.
Barnsley turned in a performance typical of a side with nothing to play for and struggled to make any impact throughout.
The Hornets kicked off knowing that they would probably have to win all four of their remaining games to stand a chance of sneaking into the play-offs and their urgency was rewarded as they took the lead in less than a minute.
Don Cowie delivered a corner from the right and after Troy Deeney hit the crossbar with a powerful header, Eustace was on hand to prod in from point blank range.
Luke Steele had to save another Eustace header as the hosts made a flying start before Matt Hill flashed a header wide at the other end.
Barnsley had done well to contain top scorer Danny Graham during the opening exchanges, and when he did find space to fire in a decent effort defender Kieran Trippier made a brave block.
The Tykes were failing to deal with Cowie's corners however and from another fine ball in Deeney volleyed wide.
Graham then chipped in a cross for strike partner Marvin Sordell just before the break but the youngster headed over the top.
Barnsley made a change during the interval as Marlon Harewood was replaced by Reuben Noble-Lazarus but it was Watford full-back Lloyd Doyley who had the first effort when he skidded a shot wide.
Deeney then wasted another decent opening when he fluffed Piero Mingoia's pass into the arms of Steele before Noble-Lazarus finally tested Scott Loach in the Watford goal with a 25-yard drive.
Jacob Butterfield saw a corner fired over the top by Bobby Hassell as the visitors mounted some late resistance.
Loach was again in action moments later to kick away an effort from Danny Haynes before Watford substitute Andreas Weimann ran clear but hit his effort across the face of goal.
Watford held out to claim the points and head to Leicester on Monday with their season still alive.
However, with games against champions-elect QPR and strugglers Preston to come after that Mackay's side's chances of gatecrashing the top six remain slim.