Brendan Steele, who led the tournament after day one, was just four strokes off the lead at 8 under.
Kevin Streelman shot the best round of the day with 6 under. Besides Moore, Angel Cabrera, who finished the day at 7 under, Jhonattan Vegas, Nick Watney, Garcia and 2012 Travelers Championship winner Marc Leishman also shot 65 on the day.
Bubba Watson and Jason Day finished the third round at 4 under while John Daly went into the clubhouse at 2 under.
The golf course at the TPC River Highlands in Cromwell was packed with hundreds of spectators on Saturday. It was in the upper 70s and low 80s on Saturday, and WFSB meteorologists said it was dry and warm.
Even though the temperature outside wasn't too hot, there have been quite a few spectators who have visited the medical tents.
"[We] can't be a more perfect weekend," said Jen Holland of Branford.
St. Francis Hospital workers were out on the course all week. They worked with an eight-bed treatment tent, a command trailer and many mobile teams along with three medical tents.
They treated about 200 people on Saturday for a variety of issues.
"A lot of things with the heat exhaustion, fatigue, not feeling well, headaches, a lot of blisters, people not wearing the right footwear for a golf course," said John Quinlavin, who is the director of emergency services.
Officials at St. Francis Hospital had treated about 450 people since the tournament started on Monday. They said those numbers are average for tournament and have treated much more people in years before.
But not everyone needed to head to the medical tent to stay cool. Ben & Jerry's was selling massive amounts of ice cream on Saturday.
"I was up at the entrance first, and there was a ton of people coming through," said Megan Parker, who works for Ben & Jerry's. "And up here there is usually a line, but it's slowing down. But once the bigger guys come to the 18th it will be a lot busier."
Also, to keep cool, free water stations were also set up so fans could enjoy golfing at its finest.
"I think it's perfect out," said Nicole Elliott of Burlington. "It's just a beautiful day today, perfect temperature, not too hot, not too cold. There is a light breeze out there, so we have really enjoyed walking around. It's been a lot of fun. Do you have sunscreen on? I do. I put my spray on and I'm good to go."
Copyright 2014 WFSB (Meredith Corporation). All rights reserved.
Ryan Moore leads after round 3 at the TravelersMore>>