Rory McIlroy has carded a second-round 65 at the World Golf Championship event in Mexico to storm ahead at the midway point of the competition.
Sullivan's day was kick-started by holing from the 9th fairway for an eagle.
LPGA: Inbee Park birdied the last hole to take a one-stroke lead over Michelle Wie and two others at the LPGA's Women's Champions in Singapore.
The Northern Irishman is nine under after a round that included an eagle, as he holed out from 151 yards on the par-four 14th, and six birdies.
Thomas is seeking his fourth victory of the 2016-17 season while world No. 1 Johnson is making his first start since winning the Genesis Open at Riviera two weeks ago.
Aguero double helps City hammer Huddersfield after early scare
He added: "It is a breakthrough for the club to say that but I do not want to think about what will happen to my future. Meanwhile, Huddersfield boss David Wagner felt his side didn't demonstrate their best qualities at the Etihad Stadium.
"I'm in a great position, but I felt like I could have been a few more ahead", said McIlroy.
Mickelson proceeded to post a 68 for a seven-under total but even his renowned brilliance was only good enough to put himself in a tie for second for England's Ross Fisher on seven-under, with McIlroy enjoying a two-shot lead. He does need Dustin Johnson to finish fifth or worse, but it'd be a moot point if he doesn't take care of his own business either way. "I think the more rounds you play out here, the more you can kind of get dialed into trusting your numbers in this altitude".
Mickelson's long-time caddie, Jim "Bones" Mackay, lasted just three holes of Friday's second round before being forced to leave the course due to a stomach virus which has affected several players in Mexico City. "My body is in great condition and if I keep playing well, I have a chance going into the weekend".
Although not having the best of tournament so far, Spieth managed to provide the moment of magic on the 16th hole on his third shot, when he aimed left to right, ultimately resulting in his favour.