The Steelmen poured forward, Jim O'Brien skipping past Michael Howard before providing a delightful chip for Murphy to head in with his first touch of the night.
The result was sweet revenge for the Scots, after Stuart Jones' goal at the Excelsior Stadium last week gave Gannon a horrendous start to his Motherwell reign.
The Steelmen now face a two-leg second qualifying round match against Albanian outfit KS Flamurtari Vlore.
Llanelli: Ashley Morris, Phillips (Moses 80), Stuart Jones (Jenkins 67), Thomas, Howard, Mumford, Venables, Corbisiero, Legg (Warlow 76), Follows, Griffiths. Subs Not Used: Craig Morris, Bowen, Holloway, Craig Jones.
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