Barnet’s task was an uphill one from the start as Mark Cousins was sent off within three minutes after pulling down a Braintree forward.
Morton stepped up against Rihards Matrevics, making his pro-debut as a result of the sending off, and scored.
Lyons-Foster had a chance from close range soon after but turned it over the bar.
The Bees first chance came when Medy Elito played in Shaq Coulthirst but his quick effort was deflected wide.
Matrevics produced a good save to deny former Bee Justin Amaluzor at his near post. The resulting corner provided Ricky Gabriel a chance to score from two yards out but he struck the crossbar before Morton hit the post from equally close range.
Craig Robson had a header cleared off the line before Morton went up the other end and made it two 34 minutes in with a good finish after he dispossed Dan Sweeney.
Braintree were lucky not to be reduced to 10-men soon after, Gabriel’s tackle on Jack Taylor was reckless and off the ground but only deserving of a yellow in the eyes of the referee.
After the break, Sweeney’s clearance struck Amaluzor and went just wide of the post.
In the 55th minute, Danny Rowe had the ball squared to him 10 yards out in acres of space but he somehow cleared it out of the ground.
Jack Taylor then had a header saved by the Braintree keeper before the hosts were given an oppotunity to make it three.
A spot kick was awarded when Robson was adjudged to have fouled his marker in the box, Morton stepped up and bagged his hat trick.
Amaluzor, desperate for a goal against his former club, was then denied by a fine save from Matrevics who flew across his goal to palm the forwards fine first time volley away.
It was four in the final ten minutes as Barnet committed forward and were caught on the counter. Iffy Allen, another former Bee, had time and space to slot past Matrevics.
Barnet – Cousins, Alexander, Johnson, Reynolds, Robson, Adams, Coulthirst, J. Taylor, Elito (Walker 39, Harrison 45), Sweeney, Mason-Clark (Matrevics 5)
Unused – Sparkes, Tutonda
Attendance – 700