The former Birmingham player opened the scoring in the ninth minute, coolly stroking home a left-footed penalty after Mark Bradley had been brought down by Dean Sinclair.
Mooney forged a good partnership up front with Michael Ricketts, who was returning for his second spell at Walsall.
The former England striker might well have had a hat-trick, but in the 32nd minute his fine shot on the turn from 20 yards was saved by keeper Shane Higgs.
Three minutes later Ricketts saw a header hit the underside of the bar, with the ball being cleared by Shane Duff and in the second half Higgs again saved as Ricketts tried to send a shot over him from 12 yards.
Cheltenham, although trying hard, seldom threatened the Walsall goal although striker Paul Connor put in a lot of good runs which came to nothing.
In the 56th minute Mooney put Walsall further ahead with a clever chip over Higgs following a good cross by Edrissa Sonko.
The Robins staged a strong finish in which substitute Ashley Vincent saw an 80th-minute header go just over the bar from a free-kick by Alan Wright.
In the dying seconds the visitors almost pulled a goal back when another substitute, Adam Connolly, saw an angled shot hit the foot of the Walsall post.
It was not a happy start for Keith Downing, appointed as Cheltenham's permanent manager on Friday, because his side never troubled home keeper Clayton Ince, while Walsall could have won by a far larger margin.