Second-half strikes from Craig Reid and Luke Freeman secured the win after Clayton Donaldson and Sam Saunders both squandered golden opportunities from the spot for the Bees either side of half-time - the former rattling the bar, the latter the post. But, instead of being 2-0 up, Brentford were soon 2-0 down thanks to Reid's smart turn and shot and Freeman's stunning 25-yard drive in the space of nine second-half minutes.
Saunders' late free-kick wasn't enough for him to make amends as Stevenage moved up to sixth with a two-point cushion over seventh-place Notts County, and Smith breathed a huge sigh of relief.
"The nerves are frayed. It's not often that you concede two penalties and come out winners. But equally, it's not often that you concede two penalties at home," he said. "I was a long way from the second one, and I have to say, it did seem like a penalty. But my one question was did Jon Ashton get anything on the ball?
"The two goals in the second half gave everyone a lift. It's great to see one of our forwards score again and Luke's strike was fantastic.
"And there were moments late on in the game where the defenders had to do their job. But all in all, everybody played their part and Lady Luck shone on us."