The 35-year-old American made the most of ideal scoring conditions at the TPC Four Seasons Resort Las Colinas, firing a flawless six-under-par 64 to grab a one-shot lead.
Australian Marc Leishman recorded a pair of eagles on his back nine to card a 65, ending a surprisingly calm day level with Germany's Alex Cejka who posted a bogey-free round.
Americans Scott Piercy, Charley Hoffman, Bill Lunde and Matt Kuchar, the world number five who won the Players Championship on Sunday, were among a group of seven players knotted on 66.
Though Palmer struggled with his driving over the last four holes on the challenging layout, he was delighted to stay at the top of the leaderboard, largely thanks to his superb short game.
"I had big pull hooks on my last four tee shots and I fought my way in," the Texan said after making three birdies on each nine.
"I kind of locked up on my tee shots, but that's what the short game is there for, and fortunately it was good today. It's great to be in this spot again.
"Continuation from last year, that's what's cool about the whole thing. It was great. I felt great all morning, warm-up was great. I knew everything was going in the right direction.
A three-time champion on the US PGA Tour, Palmer was beaten by compatriot Keegan Bradley on the first extra hole of last year's Byron Nelson Championship. This week, he is determined to respond in the best possible way.
"I keep telling myself, 'Redemption!'," Palmer smiled. "I didn't lose it last year by any means, but to get back in the same setting with the same people watching, here where I live, and just to have that feeling again....
"This time I want to be the guy standing with the trophy. That's been my focus ... leading up to the start of this tournament."
Leishman, who is bidding for his first victory on the US PGA Tour, chipped in to eagle the par-four 11th and holed an eight-foot eagle putt at the par-five 16th to rocket up the leaderboard.
"It's nice having a real good chance for eagle, doesn't happen a whole lot," he said. "Both of the opportunities for eagle I had I was thinking about holing, and it's nice when they go in.
"I'm just trying to do what I can to give myself a chance (to win) really," added Leishman, who has twice been a runner-up on the US PGA Tour at the 2009 BMW Championship and the 2010 Farmers Insurance Open.
Bradley launched his title defence with a 67 while American world number 10 Phil Mickelson and former world number one Ernie Els experienced mixed fortunes as they carded 70s.
Left-hander Mickelson offset two birdies with two birdies, including his final hole where his drive and approach shot each ended up in bunkers, while South African Els clawed his way back after a bogey-bogey start.
"I'm frustrated that I'm letting shots slide here or there and I'm not capitalising on some birdie opportunities," said Mickelson.
"The course is in great shape and we had a perfect day.
"There are some low scores out there and plenty of birdies but I didn't take advantage of it."