Rangers striker Kris Boyd blew two opportunities to break the deadlock in the space of three minutes, blazing a half-volley over the bar in the 12th before heading over at close range in the 15th.
Ally McCoist's side looked determined to find an opener before half time, coming closest in the 22nd minute when Nicky Law's strike from David Templeton's nod-on was deflected narrowly wide, but it was Alloa who snatched the lead.
There were chances for both sides in the early stages of the second half as Boyd headed Bilel Mohsni's ball over in the 54th minute, and Simmons nodded wide at the other end moments later.
Alloa had a great opportunity to extend their lead in the 70th minute when they broke at pace, the ball eventually falling to Greig Spence in front of goal, who shot straight at Simonsen.
Rangers came alive in the closing stages and forced an equaliser seven minutes from time through substitute Templeton, who poked the ball home from inside the six-yard box following a goalmouth scramble.
A late chance to win it fell to Boyd, but the wasteful striker bundled his last meaningful effort of the game over the bar and the match ended 1-1.