In-form Deeney struck for the ninth time in 14 games as Walsall wrapped up a comfortable victory before half-time.
Mark Bradley had given Walsall the lead with his first goal of the season, Deeney doubled their advantage before Anthony Gerrard completed the scoring in the 39th minute.
It was the perfect way for Walsall to bounce back from last weekend's 5-0 mauling at the hands of Bristol Rovers.
Shell-shocked Brighton should have gone into the game on a high after beating Yeovil 5-0 in their previous match to earn new manager Russell Slade his first win.
But they never got into gear and remain firmly rooted in the relegation zone after a dismal display in the opening 45 minutes.
The first half was a personal nightmare for Brighton left-back David Livermore who was undone for the opening two goals.
After 14 minutes he was outpaced by Alex Nicholls who crossed for Wales Under-21 international Bradley to stroke the ball home from 12 yards.
Nicholls showed Livermore a clean pair of heels again on the half-hour and this time teed up Deeney to grab his 11th goal of the season.
Any hopes of a Brighton revival disappeared in the 39th minute when the Seagulls defence failed to deal with a cross from Sofiene Zaaboub.
His centre was smashed on to the bar by Bradley and Gerrard reacted faster than the Brighton back line to pounce from close range.
Slade tried to shore up his defence at half-time by replacing the luckless Livermore and central defender Adam El-Abd with Garry Borrowdale and Tommy Elphick.
But the damage had already been done and the closest Brighton got to a consolation was six minutes from time when Dean Cox got their first shot on target only to be denied by goalkeeper Clayton Ince.
Walsall should really have raced to an even more comprehensive win but striker Jabo Ibehre wasted two golden chances when he only had goalkeeper Mikkel Andersen to beat.