Murray had trailed overnight leader Morrison by a single stroke at the start of play but erased the deficit on the front nine after he birdied the par five third for the third consecutive day.
Morrison also birdied the third but his advantage was lost with a bogey at the par five sixth to leave the English Challenge Tour graduate level with his playing partner.
The duo were two shots clear of nearest rival Simon Thornton. The Irishman, whose wife is expecting their first child today, mixed a pair of birdies and bogeys in an eventful outward nine which produced no more than a level par 36.
England's John Parry was a further stroke back on nine under after shooting 34 by the turn.
Julien Guerrier was the day's big mover as he picked up six strokes after 16 holes to be eight under.
The Frenchman had carded seven birdies with his only blip arriving on the par four 13th to draw him level with Gary Clark in fifth place.