They head into the final round at Crosswater Gold Club with a two-stroke lead over D.A. Weibring. Tom Watson and Tom Kite were three strokes back of the leaders.
Edwards was atop the leaderboard much of the day, but double-bogeyed the par-3 17th hole and finished with an even-par 72 for a 12-under 204 total. McNulty bogeyed the par-4 18th for a third-round 70.
Weibring, who won the tour's last event, the 3M Championship in Blaine, Minn., shot a 68 to reach 10 under. He said he was not thinking about the competition going into Sunday's final round.
'I think it's up to me to play a good round.'
Keith Fergus, who won the Ginn Championship earlier this season, appeared to finish at 10 under along with Weibring. But a rules official penalized Fergus two shots for testing the conditions of a bunker on the 17th hole by shuffling his feat.
Fergus wound up 8 under after three rounds with a 72.
Edwards, who joined the Champions Tour last year and has three top-10 finishes this season, eagled the par-5 12th, hitting his third shot 146 yards into the hole.
Watson, who on Friday had a setback when he hit Ben Crenshaw's ball by accident and was given a two-stroke penalty, shot a 67 Saturday to reach 9 under.
He said he wasn't thinking about the difference those two shots could have made going into the final round.
'It's gone,' he said. 'The `What ifs?' they do no good. The only positive thing is I checked my ball 14 times today.'
With Watson at 9 under was Kite, who shot a 68.
Last year, Argentina's Eduardo Romero came from five shots back on the final day to beat Lonnie Nielsen with a birdie on the first playoff hole at the Reserve Vineyards & Golf Club in Aloha, west of Portland.
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 Vineyards & Golf Club outside of Portland.
This season, it came to Crosswater in central Oregon's high desert. Canoers on the Little Deschutes River, which cuts through the course, got to take in a little golf along with the scenery.
Money leader Jay Haas shot a 71 for a 3-under 213 going into the final round. Haas has finished in the top 10 in the season's first three majors. 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.