The pair had tied on 281 after Barnes, making his European Seniors Tour debut, holed a six-footer for a closing two- under-par 70 to Murphy's 71.
"That was one of the few putts in the last two days I actually hit," said an emotional Barnes. "Ever since I realised my first Senior Open would be at Portrush where Max won his Open, I have dreamed of this win."
The leading pair edged out the former title winner, Bob Charles, and John Morgan, Europe's top senior last year, by one shot. Charles finished with a 66, the best round of the tournament, while Morgan shot his second 68 of the week.
Tommy Horton, who battled back into the reckoning with a superb 67 yesterday, was prevented from advancing further by an unfortunate double-bogey six at the fourth. The Channel Islander had to settle for a share of fourth place with South Africa's John Fourie.
Scores, Sporting Digest, page 23Reuse content