Doug Ghim and Andrew Novak were both two shots off the lead while three-times major winner Jordan Spieth reached the turn at two-under for his round, moving him three behind Taylor.
The leaders will have 30 holes to get through on Sunday with organisers hoping the risk of frost in the morning does not add any further delays to the schedule.
A 3 1/2-hour rain delay on Thursday put the tournament behind schedule and frost on Friday added to the disruption.
Theegala had fired a seven under-par 64 to top the leaderboard after the second round but then returned to bogey the first two holes of his third round.
A birdie at the par-3 fourth, steadied him but Taylor took advantage to edge back in front, draining a 48 foot putt for birdie on the par-4 fifth.
Taylor had equalled the course record on Friday with his 11-under-par 60 and while he wasn’t able to recapture that form in his second round, making bogey on the first hole, he recovered with birdies on the 10th and 17th to shoot 70.
The Canadian finished second in this event last year, missing out to Scottie Scheffler by two shots, before going on to win the Canadian Open in June.
“I feel like I just have good vibes here after last year. I played great last year and just got beat I felt like,” he said.
“I wasn’t probably expecting to shoot a 60 or something crazy low the first day, but I figure I have good energy here now, and a lot of years in a row I didn’t.
“I wouldn’t say it’s unfinished business, but I’m definitely in good position to try to finish it off,” he added.
Theegala was one of the few players to have finished his first round on Thursday and so did not play at all on Friday.
“I felt like I had a 12-hour day the first day, nothing yesterday, and then another 12-plus-hour day today. So ready for another 10-, 12-hour day tomorrow,” he said.
“It’s been a weird week, and I’m actually really exhausted right now. It’s not often you play two days of — not necessarily even a lot of holes but just a lot going on,” he said.
There was no shortage of energy around sold-out TPC Scottsdale, with the traditional raucous crowds at the “stadium” par-3 16th.
However, organisers were forced to take the drastic measure of briefly halting sales of alcohol and even turn away some fans as chaos ensued.
“Due to larger than usual crowds, the WM Phoenix Open entrance gates are temporarily closed and shuttle service to the event is on hold,” organisers said on social media.
“Shuttle service back to parking lots will remain running. Regularly check our channels for updates.”
The decision to halt booze sales left fans rather upset, sparking a chant of “we want beer”.
However, several videos that popped up on social media proved officials were perhaps right all along to stop selling alcohol.
Many fans decided it was the perfect time to strip off their shirts and slide in the mud, much to the joy of those in the immediate vicinity.
Another took things a step further, running onto the infamous 16th hole and flipping into a bunker.
With the partying crowds roaring every great shot or putt but booing and jeering missed putts and off-target approaches, the noise at the hole has become synonymous with the Scottsdale event.
“Just hearing the cheers is pretty epic. A bunch of guys with my name and my face on shirts out there. The officer was telling me people got too drunk. But it was all in good fun, and hopefully everyone stayed safe,” said Theegala.
“It’s a blast. There’s definitely some people that aren’t the best drunks, but for the most part it’s all positive, and it’s a fun atmosphere.
“You do have to block some of it out at certain times. That’s for sure. But still kind of in full embrace mode.” he added.