Jimenez birdied the par-4 15th and par-5 17th in a bogey-free 5-under 67 that got him to 12-under 132 in the PGA Tour Champions event at The TwinEagles Club.
''I have to say happy because I make 5-under par,'' the 53-year-old Spaniard said. ''But hitting 18 greens today and played so solid and so many chances for birdie looks and feel like I missed something on the golf course. I left something on the golf course today. ... You need to be there inside my skin to feel all the chances for birdie today.''
Couples shot a 65 in perfect conditions on the Talon Course. He bogeyed the par-4 18th after making birdies on Nos. 14, 15 and 17. The Hall of Famer won the 2010 event at The Quarry.
''It was a good day,'' Couples said. ''I bogeyed the first hole and I bogeyed the last, and in between was beautiful golf. Come out tomorrow firing and hopefully have another good round.''
Sutherland had a 63 for the best round of the week. He was 6 under on the final eight holes, making a birdie on the 11th, an eagle on the par-5 13th and closing with three straight birdies.
''I have a lot of confidence in how I'm playing and today it kind of all came together,'' Sutherland said. ''I hit a lot of good iron shots and I putted really well. ... I made a few 20-footers, but I made a lot of putts inside 10 feet. Those putts aren't gimmees. Hit good putts.''
Jimenez will play alongside Couples and Sutherland in the final group.
''It will be nice,'' Jimenez said about Couples. ''He's a nice player and the people love him - and I love him, too.''
Jimenez has three victories in 23 career starts on the 50-and-over tour, winning once in each of the last three seasons. He won the last of his 21 European Tour titles in 2014.
Bob Tway (68) and Doug Garwood (70) were tied for fourth at 9 under.
Defending champion Bernhard Langer was 7 under after a 68.
''Mostly pluses,'' Langer said. ''It was a bit lackluster in a sense. Just couldn't make any putts. Just never really got a lot of momentum.''
Also the winner in 2011 at The Quarry and 2013 at TwinEagles, the 59-year-old German star won the season-opening event in Hawaii for his 30th tour victory. He has 28 rounds in a row under par.
Colin Montgomerie ran his under-par streak to 29, shooting a 67 to get to 6 under.
John Daly followed his opening 68 with a 74 to drop into a tie for 38th at 2 under.