Murtagh was at his consistent best from the Nursery End on the final day, sending down 26.2 overs for his 6/60 in Lancashire's second innings, dismissing key men Jos Buttler and Ashwell Prince along the way.
That pair had threatened to frustrate title chasers Middlesex during a fine sixth wicket partnership of 118, which took the visitors almost to the Tea interval from a dire position of 45/5 in the first hour.
But Buttler was dismissed for 50 and Tom Smith edged Murtagh behind three balls later to reignite Middlesex's victory charge.
Captain Glen Chapple rallied with 32, but it was Murtagh who struck the lethal blow, tempting Prince into a loose shot outside off stump to dismiss the former South Africa batsman for a gritty 86.
Lancashire were all out shortly afterwards, leaving Sam Robson and Chris Rogers with the easy task of knocking off just 31 from 20 overs in bright evening sunshine, to propel Middlesex back into the title hunt.