Playing the back nine first on a chilly day at the Harbour Town Golf Links in Hilton Head Island, South Carolina, Taylor birdied two of his first six holes but gave the shots back with a double-bogey at the 16th and a bogey at the first.
He recovered nicely with three birdies on his next six holes before ending his round in spectacular fashion with an eagle at the par-four ninth for a four-under 67.
"I was trying to decide between a lob wedge and a sand wedge, but I had a little bit of an upslope lie, I decided to go with the sand wedge and hit a smooth one," Taylor said about his eagle from 100 yards out. "Came off right, right at it, and fortunate enough to go in."
Campbell, without a top 20 finish this season and chasing his first US Tour win in five years, got his round off to a blazing start with four birdies in his opening seven holes.
The 2003 US PGA Tour champion wobbled around the turn with bogeys at the eighth and 10th holes sandwiched around a birdie at nine but was error free the rest of the way.
Knost, without a US PGA Tour title on his resume, had three birdies over his final five holes, including the 18th, to earn a share of the lead.
American journeyman Jim Furyk, who is trying to return to the winner's circle for the first time since 2010 when he walked away with The Heritage winner's Tartan jacket, was among a group of four golfers sitting one shot off the pace.
Defending champion Brandt Snedeker, who beat British world number one Luke Donald in a play-off last year, opened with an even-par 71.
Donald could not find any form on one of his favourite layouts, mixing a single birdie with a double-bogey and three bogeys for a four-over 75.
Matt Kuchar, who was tied for the lead in the final round of the Masters with three holes to play only to finish in a tie for third, tried to carry some of that Augusta National momentum into Hilton Head but settled for one-over 72.
Northern Irishman Padraig Harrington and Swede Henrik Stenson were two other players suffering from Masters hangovers, both returning three-over 74s.
Harrington, who made a late charge for the green jacket, had one birdie against four bogeys while Stenson, who tumbled from the top of the leaderboard with a quadruple-bogey eight on 18 in the opening round at Augusta, had another disastrous finish with a double-bogey at 13 and bogeys at 15 and 16.
European Ryder Cup captain Jose Maria Olazabal, who was caught speeding last week, had a slow start to the tournament with three double-bogeys, two bogeys and two birdies for a 77.