'Gary Player always said, `Mark, as long as you win by one, you've won,'' McNulty said.
McNulty double-bogeyed the 18th hole at Crosswater Golf Club, but still claimed his first major by five strokes.
McNulty shot a 4-under 68 Sunday, finishing the Champions Tour event with a 16-under 272 total. David Edwards, tied for the lead with McNulty after the third round, had a 73 to finish at 11 under. D.A. Weibring was 10 under after a 72.
The day started out rainy in central Oregon, but later in the final round there was mostly brilliant sunshine. The wind gusted and temperatures were on the chilly side, ranging from the 50s in the morning to the low 60s in the afternoon.
McNulty, who had six birdies on the final day to go along with his double bogey, has had lower back problems and had not finished in the top 10 this season.
He birdied four of the first seven holes, setting him on the course for victory.
'It was my tournament to lose, but I still had to earn it,' he said.
He splashed on to the Champions Tour in 2004 and was named rookie of the year. With Sunday's victory, he has six total victories on the tour for players 50 and older.
Before joining the Champions Tour, McNulty played primarily on the European Tour. His best finish in a major was when he tied for second with Payne Stewart in the 1990 British Open, five strokes behind of Nick Faldo.
McNulty was steady all day and didn't even show much emotion, except on the troublesome 18th, when he missed a nearly 4-foot putt.
'Fortunately, I have a lock,' he joked with the gallery.
'Today I was at ease,' he said about his cool demeanor. 'It was quite unbelievable how fortunate and lucky I was. I didn't feel any jitterbugs as all.'
Edwards, who joined the Champions Tour last year and had three top-10 finishes before The Tradition, had four bogeys and three birdies in the final round. Edwards and McNulty went into the final day with a two-stroke advantage.
Edwards said his back was giving him trouble all day, perhaps because of the weather.
'So I didn't hit very many shots to warm up and I didn't practice any at all after the rounds,' Edwards said.
McNulty is the second straight international player to win the event. Last year, Argentina's Eduardo Romero beat Lonnie Nielsen with a birdie on the first playoff hole at the Reserve Vineyards & Golf Club in Aloha, west of Portland.
Romero finished this year with a 3-under 285.
The Tradition started at Desert Mountain in Scottsdale, Ariz., before it was moved to Superstition Mountain. With the help of Oregon native Peter Jacobsen, the event moved again in 2003 to the Reserve. This season, it came to Crosswater in central Oregon's high desert.
Money leader Jay Haas also finished at 3-under 285. Loren Roberts, who won The Tradition in 2005, and Tom Kite each finished at 8 under.
The Tradition is the fourth of five majors on the Champions Tour. Tom Watson won the British Open, Brad Bryant took the U.S. Senior Open and Denis Watson won the Senior PGA Championship.
The Tradition is sponsored by JELD-WEN, an Oregon-based window and door manufacturer.