Marlon King laid the ball off for Henderson to score from the edge of the box, before Mackay touched home Anthony McNamee's inswinging free-kick.
Ben Foster made two good saves for Watford, who had Ashley Young red carded for kicking out at Kevin Foley.
Watford manager manager Adrian Boothroyd:
"We are learning to manage games, and the best teams are the ones who know how to manage games.
"It was a good win, but it wasn't a particularly good performance.
"We needed this result, because it gives us momentum. However, we have a lot of work to get through on the training ground."
Luton: Beresford, Foley, Underwood, Heikkinen, Barnett, Edwards, Brkovic (Showunmi 62), Robinson, Nicholls, Howard, Vine (Feeney 76).
Subs Not Used: Perrett, Morgan, Brill.
Goals: Edwards 49.
Watford: Foster, Doyley, Chambers (DeMerit 74), Mackay, Carlisle, Young, Mahon, Bangura (Spring 77), McNamee (Stewart 58), Henderson, King.
Subs Not Used: Chamberlain, Devlin.
Sent Off: Young (67).
Booked: Henderson, Carlisle.
Goals: Henderson 9, Mackay 30.
Ref: I Williamson (Berkshire).