Musselburgh got off to the worst of starts when the visitors took the lead after only two minutes when Kevin Fotheringham was left unmarked three yards out and he met a corner kick to head powerfully into the net.
However, Musselburgh equalised after twenty five minutes when they were awarded a free kick just outside the box and Alan Morgan curled the ball over the wall past the goalkeeper.
The game flared up on the stroke of half time when a melee developed outside the Musselburgh box and referee Hogg showed a straight red card to Burgh's Chris Gray for an off the ball incident.
Despite being a man down in the second half Musselburgh more than held their own and limited the visitors to shots from outside the box.
Fifteen minutes from time, Hill of Beath almost regained the lead when a Mike Gemmell free-kick deflected off Stuart Fraser and struck the post with the keeper beaten.
In the final minute, Gemmell again had the chance to secure the points but his header from close range went inches past the post and, in the end, both teams had to settle for a point.
Musselburgh Athletic: Renton, Gordon, Noble, Fraser, Kerr, Morgan, Russell (Shand 57), Beveridge, King, Gray, Draper(Porteous 85). Subs: Gourley, Ramage, Adams.
Hill of Beath: Hall, Haddow, Morrison, McCulloch, Adair, Fotheringham (Seeley 70), Wright (Hay 85), Gemmell, Smith, Bathgate, Maxwell. Subs: Lowe, Paterson, Beveridge, Adamson, Marshall.
Musselburgh Athletic 1
Hill of Beath 1