Latics came away from London with a point, after taking the lead, and then going behind at Grosvenor Vale.
Joe Nuttall opened the scoring for Oldham after receiving the ball from Mark Shelton and going around the goalkeeper.
Two early goals in the second-half put the hosts ahead, but when Nuttall was fouled in the box, he stepped up and put the ball past Howes from the spot.
Both sides had a number of chances during the opening periods of the game, as they looked for an early opener.
Rooney played Sambou through, before the Crewe loanee cut in and fired his shot over the bar.
The hosts worked the ball well into the 6-yard box, just for a goalline clearance from Oldham to deny them, only a few yards out.
Latics eventually opened the scoring thanks to Nuttall.
Shelton’s sublime pass from deep inside the Latics half took the entire Wealdstone defence out of the game, leaving Joe to run around Howes and slot home.
Nuttall nearly scored his second moments later, from a similar position, but a last-ditch tackle from Barker took the ball from under his feet.
Green found himself in a good shooting position, but his effort from a tight-angle was pushed wide by Howes’ hand.
Wealdstone came out in the second-half with attacking intent, and found an equaliser when Olomola pushed the ball onto his left foot as he advanced into the box, finishing past Hudson from close-range.
The game was turned on its head ten minutes later when Obiero picked out Lo-Everton inside the 6-yard box, who put the ball beyond the reach of Hudson.
Unsworth immediately made two changes, Peter Clarke and Ellis Chapman came on in place of John Rooney and Devarn Green.
Latics won a penalty when Stones ‘keeper Howes brought down Nuttall in the box, with the England C internation converting from the spot, getting his second of the game.
With the score now level, Unsworth’s side looked for a winner.
Shelton attempted another deadly pass, this time a ball over the top for Sambou, but it was just a tad heavy for the striker, as Howes scooped up the ball.
Substitute Fondop nearly won the game at the death, he got on the end of Sutton’s looping header, but could only nod it over the bar.
Latics: Hudson, Hogan, Sheron, Green (Chapman 58), Shelton, Rooney (Rooney 58), Sambou (Fondop 71)), Kitching, Sutton, Yarney, Nuttall