Open champion and Barseback member Henrik Stenson birdied two of his last five holes to card a level-par 73 which was matched by defending champion Matt Fitzpatrick, while BMW PGA Championship victor Alex Noren struggled to a 75.
And Summerhays pounced with a four-under-par 68 to take control heading into Sunday's final round.
Spieth had eight birdies, which was tied with Lingmerth, Summerhays, and Rickie Fowler for the most in the first round.
The 33-year-old from Utah, who finished third in last year's PGA Championship, trailed midway leader Jason Dufner by five shots overnight but five birdies - and a bogey on the 13th - saw him move into the outright lead on 13 under par ahead of 2013 victor Matt Kuchar.
From 175 yards out, Dufner looked to improve upon the bogey from Thursday's round and did so in a big way, playing his shot off the slope to the back left of the pin and rolling it in for eagle. He three-putted from 4 feet on the sixth hole for a double bogey.
"I have no idea what tomorrow is going to hold, but I feel pretty good about the process and the shots that I'm able to hit right now". Spieth and Justin Thomas (71) were tied for fourth, eight shots behind.
Lingmerth had no such problems: "I caught some breaks when I missed the fairway and still had some fairly good opportunities from the rough", he told golf Channel. "Even if it doesn't shake out how I want to [Sunday], I think I'll be like, 'Oh, where's the next hole I need to go play?"
Zach Johnson dug deep to make the cut on the number with four birdies on his last five holes. He had played great golf his first two rounds, shooting 66-69 to get to nine-under for the week.
The 33-year-old hit 13 of 14 fairways and said sustaining his career-best form with the driver would be key to any hope of catching Dufner. "I can always get into the top five and there's a lot of FedEx Cup points and prize money at stake", said Leishman. It added to a 71, and he was six shots behind.
Sweden's David Lingmerth, the overnight co-leader with Dufner, followed up his opening 65 with a two-over 74 and was in a group of six players on 139 that also included Scotland's Martin Laird, Argentina's Emiliano Grillo and two-time Masters champion Bubba Watson. He has missed the cut three times.
Creamer won the last of her 10 LPGA Tour victories in 2014 in Singapore when she made a 75-foot eagle putt on the second hole of a playoff with Azahara Munoz. Matt Kuchar (70), Bubba Watson (68), Kevin Kisner (69) and Argentina's Emiliano Grillo (68) are also on five under.
World No.3 Jason Day has cursed sluggish starts at his hometown event but is desperate to find consistency in his final hit-out before the US Open.