Referee Fred Graham pointed straight to the spot in stoppage time, ruling that Paul Downing had brought down James Tarkowski, but O'Donnell flew to his right to pull off a great save from substitute Adam Rooney's well-struck penalty.
Smith's side moved into the League One play-off zone with the victory, and Smith said: "He's an improving goalkeeper and that's why we gave him an extended contract recently. But I'm not sure if it was a penalty. Paul (Downing) said he never touched their player."
O'Donnell, a former Sheffield Wednesday goalkeeper, made three other crucial saves when impressive Oldham were on top, and Latics' manager Lee Johnson groaned: "I thought we should have had all three points.
"We were fantastic, in passing and movement, but if you don't score you don't win. It's unbelievable. We've hit the post and bar in the second half. I can count at least 10 chances and goalscoring opportunities we created in the match.
"We really camped on them (Walsall) in the last few minutes, and what else can you do? It was a match when I would give all my players eight or nine for that performance.
"I thought the game was a very good advert for two clubs with small budgets, really trying to play football in the right way with young and energetic players."
Rooney missed one other great chance before the penalty, and Johnson said: "He has to lift himself up and kick on so when the chances come next time he buries them."
When the ball broke to Sam Mantom just outside the box he smashed a first-time drive past Mark Oxley, who had not been troubled too often. That was Mantom's third of the season.
Saddlers boss Smith added: "It was perhaps an undeserved win and probably a draw would have been the right result. We didn't play anywhere near as well as we can, but there have been games this season when we have deserved all three points and haven't got them.
"All credit to Oldham, they played some terrific football in the first half and we had to defend...a bit too deep for my liking, and we addressed that at half-time.
"But it's pleasing for us to be in the play-off zone, which is the fruits of our labour and a hard-fought win.
"Febian Brandy showed some good little touches and is capable of giving us something different."
Brandy was booed by the Walsall fans when he was at the Banks's Stadium with Sheffield United a fortnight ago, but enjoyed a much better reception this time around.
Walsall now face another tough home game on Saturday when table-topping Brentford are the visitors.