Walsall were indebted to veteran goalkeeper Jimmy Walker after they held Stevenage to a goalless draw.
Luke Freeman forced the first of a string of fine saves from Walker with a powerful strike.
Adam Chambers drew a smart save from home keeper Chris Day after Chuks Aneke had volleyed just over for the hosts.
Freeman was again thwarted by the in-form Walker and Saddlers striker Jon Macken missed a great chance to win it when he fired over.
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Stevenage manager Graham Westley told BBC Three Counties Radio:
"I think there was a winner and they were the conditions. It was very, very difficult. The wind was swirling around out there and it was difficult for either side to play any good-quality football.
"We certainly had the better chances throughout the game, that's for sure.
"It was probably one of those days, where despite the eight or 10 chances we did create, we didn't manage to put one away."