On a day when American John Catlin was penalised for slow play - the first such penalty issued at a major since the 2013 Open at Muirfield - Conners carded a splendid five-under-par 67 in 10-15mph winds on the Ocean Course on the South Carolina coast.
As only seven players managed to shoot in the 60s, the superb ball-striking effort earned the 29-year-old a two-shot lead from a six-strong group that includes two former winners, Brooks Koepka and Keegan Bradley.
Alongside them in that chasing pack are another American, Aaron Wise, as well as Norwegian Viktor Hovland; England’s Sam Horsfield and Australian Cam Davis.
Defending champion Collin Morikawa posted a solid round of 70, as did Scot Martin Laird, five-time major champion Phil Mickelson, 2019 US Open champion Gary Woodland and four others.
Conners, who has recorded seven top-10 finishes in 20 starts on this season’s PGA Tour, had one blemish on his card, a bogey at the par-4 ninth.
He still made the turn in 34, then picked up on birdies at the 11th, 15th and 16th holes to become the first Canadian to lead in a men’s major since Mike Weir was also out in front after day one in the 2009 US Open.
“I kind of started the day thinking, ‘why not me?’” said Conners, who tied for seventh at the Players Championship and tied for eighth at the Masters earlier this year. “There’s birdies to be had. Just play with patience. You know, take advantage of the opportunities when they present themselves.”
He needed only 24 putts in his opening round, making a 33-footer for birdie at the par-3 fifth and burying a key 55-footer from just off the front of the difficult par-4 15th.
Conners played his last five holes in two-under and nearly added one more birdie at 18, but missed a chance from 13 feet.
“I knew those holes were difficult,” he said. “As soon as you make the turn back into the wind on 14, the last few holes, they are all beasts.”
US Open champion Bryson DeChambeau sits 31st after a 72, the same as world No 3 Jon Rahm, while top-ranked Dustin Johnson only mustered one birdie as he had to settle for a 76.
Catlin, who plays on the European Tour, sits a shot ahead of Johnson after he was hit by a rare slow-play penalty on his major championship debut,
The recent Austrian Open winner received a pace-of-play warning on the 16th hole, seventh of the day, after taking 74 seconds for his second shot.
When he then used 63 seconds for his second shot at the third, he was deemed to be in violation of Rule 5.6b (3) and was given a one-shot penalty.
He is the first player to be penalised in a men’s major since Hideki Matsuyama during the third round of the 2013 Open in East Lothian while Frenchman Gregory Bourdy was the most recent player to be hit for slow play in the US PGA Championship, in 2010 at Whistling Straits.