Orient, playing their first match for three weeks, were outplayed at Withdean Stadium with Brighton consolidating their position at the top of League One and getting their first league win in six games.
Murray struck in the 29th minute with a low-shot in to the bottom corner following a cross by Chris Wood. The lead was extended two minutes later when Orient keeper Jamie Jones, caught off his line, could only palm a goalbound cross from Wood into the roof of his own net.
Murray put Brighton firmly in control five minutes after the interval with a well worked goal, finding the net from close range following a pass by Liam Bridcutt. And he completed his hat-trick after an hour, getting in front of keeper Jones to slot in a pass from Elliott Bennett and extend his goals tally for the season to 10.
Substitute Ashley Barnes, who came on to replace Murray, put the finishing touch to Brighton's emphatic victory 17 minutes from time from close in after his initial header was saved.
Orient were denied a late consolation when substitute Adam Chambers cannoned a shot against the post.