Up by one shot, he was not confident he'd be there at day's end, predicting Kenny Perry - who had six holes to play - would be ahead by three shots.
Perry made just one birdie down the stretch at the TPC Twin Cities to shoot his second straight 65, leaving him tied at 130 with Goydos and Gene Sauers heading into Sunday's final round. Sauers shot an 8-under 64.
''It's funny, you can shoot a pair of 65s, be 14-under and they're catching you,'' Perry said.
Goydos, who shot 59 at the PGA's 2010 John Deere Classic, was 7-under through 12 holes, before birdies at 15, 16 and 17 and an eagle on the par-5 18th.
''It was just one of those weird days,'' he said. ''The whole key to that round was to stay completely out of your own way and let whatever happens, happen. I did a pretty good job of that.''
Mike Goodes, a co-leader with Perry after round one, shot 68 and was one of seven players trailing by three shots.
''Anybody as far as four back can win this golf tournament,'' said Perry, who won this event in 2014 and 2015. ''I'm going to have to figure out a way to go out there and shoot another 65 and see where that stacks up. It's going to be a birdie-fest. . There's going to be a lot going on out there tomorrow.''
With little wind on a roomy course that received 1.15 inches of rain Thursday leading to soft greens that still play fast, 66 of 77 players bested par, with an all-time tour-record 56 shooting in the 60s. The day's scoring average of 67.88 is also the lowest in tour
Goydos knew a good round was possible after needing three shots to get on the first green, but one-putting for a par. He needed one putt on 16 greens and two on the others.
In comparing his two lowest rounds, Goydos believes he hit the ball better seven years ago, but did not putt as well.
''I started out making 10-footers for birdies, then 12-footers, then pretty soon I'm making 20-footers. I just kept getting farther away from the hole,'' he said. ''Normally, it's the other way, you start getting more confidence as you start getting closer to the hole down the stretch when you shoot a really good one. I went the other way, started hitting it farther away and still making it.''
The winning score at the 3M Championship has been at least 15-under for 10 straight years. The tournament record is 25-under by David Frost in 2010.
''You know there's going to be good scores, and there's a bunch of good scores,'' said Stricker, who got just one practice round before the tournament. ''It didn't seem like this course was a gimme where every hole you're going to birdie kind of attitude.'