Star battled to a 2-1 victory against a decent Broxburn side on a bitterly cold day at New Victoria Park, where the visitors were very unlucky not to take the lead after just four minutes.
Craig Young curled in a dangerous free kick that deceived everyone before smacking off the face of the back post, before Blair Tolmie cleared to safety.
Two minutes later. the other post was struck when a corner almost found its way straight in, but again luck was on Star’s side.
The deadlock was broken after ten minutes when Broxburn deservedly took the lead. A corner was half punched away by goalkeeper Keiron Renton but but the ball was headed back in and Fraser Keast managed to loop it into the net.
Star were level five minutes later with their first attempt on goal. Craig Matti King drove forward fully 60 yards before being chopped down 25 yards from goal, and Lee Currie curl a beauty over the wall and into the net.
Currie almost repeated his feat after 31 minutes when he fired another free kick over the wall but this time it smacked off the crossbar.
Star should have increased their lead after 50 minutes when Craig Thomson released Kris Renton down the left. His inch-perfect cross found Jono McManus all alone but the full-back lacked composure and shot over the bar.
Star finally took the lead after 68 minutes when a long ball over the top released Renton. Just as he strode into the box he was bundled to the ground by Miller who was unfortunate to see red.
Thomson made no mistake from the spot, sending ’keeper Maley the wrong way. Broxburn reacted by sending on Ross Nimmo for Marcus Millar.
Good work by Lewis Coult after 74 minutes found Renton in space. His effort beat Maley but flashed just wide.
Gary Cherrie replaced Cropley after 77 minutes and Broxburn made their last change after 81 minutes when Mike Williams replaced Kieran Anderson before Kevin Motion replaced Matti King after 83 minutes. Star continued to press for the third safety goal but could not make their numerical advantage count.
The closest they got was a Renton free-kick that went just over before the same player saw his header cleared off the line by Nimmo.