'I'm only 25 and my goal this year is to get more last-group practice,' Watson said. 'I want to get some practice with the pressure and everything and then maybe one day win a big tournament. To get into the last group is a big deal for me.'
Quinney, who won two weeks ago, carded a 4-under 67 and stands at minus-11. Forty-four-year-old Robin Byrd used a 64, that included six straight birdies on the back nine, to move into third place at 10-under-par 132.
Scott Dunlap, Scott Gutschewski and Kyle Kovacs are two strokes further back at minus-8.
Watson opened with a birdie on the first at Empire Lakes Golf Club. However, Watson cooled as he ran off nine consecutive pars before catching fire on the back nine.
The 25-year-old dropped in a birdie at the par-5 11th to move to minus-7. He came right back with a birdie at the 12th. Watson made it three in a row when he rolled in a birdie on No. 13.
Watson, a native of Bagdad, Fla., wasn't done there. He converted a birdie at the 14th to get to 10 under. His run ended with a bogey at the par-4 15th.
Watson came right back with a birdie on 16. He capped his round by rolling in a 20-footer for eagle from off the green at the par-5 closing hole to take the lead after two rounds.
'I told my caddie I wanted to hit it long and take a drop from the grandstand if I had to,' said Watson. 'It was on some dirt back there, so we decided to putt it. It did everything we wanted it to do and it went in.'
Quinney, who won the Oregon Classic two weeks ago, played the back nine first on Friday. He got going with a birdie at the 12th before carding birdies at the 16th and 18th to make the turn at minus-10.
The 2000 U.S. Amateur champion kept it going on the front side. Quinney dropped in a birdie at the par-3 second. He moved to 12 under when he drained a birdie at the par-4 sixth. However, Quinney three-putted for bogey at his final hole to slide one stroke behind Watson.
Shane Bertsch shared seventh place entering day two and after carding a 2-under 69, he now stands alone in seventh at 7-under-par 135.
Kevin Stadler, a two-time winner this season, is one stroke further back at minus-6 and is joined there by Gabriel Hjertstedt, Jeff Klauk, Ryan Armour and Mike Sullivan.
A total of 73 players made the cut, which fell at 1-under-par 141. Among those missing out on the final two rounds were Jason Buha (143), two-time winner this year Jimmy Walker (145) and 2003 champion James Oh (154).