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Mathis, who earned his 2011 PGA Tour card by finishing in the top 25 in last year's Nationwide Tour money list, took charge with a five-under-par 65 on a sweltering hot and humid day at the TPC Southwind.
Swede Robert Karlsson, beaten by Britain's Lee Westwood in a three-way playoff for last year's title, opened with a 66 to end the day level with Americans John Merrick, Kris Blanks, Colt Knost and Kevin Kisner.
World No 2 Westwood launched his title defence with a 69, salvaging a mediocre round with three birdies in his last four holes.
Mathis, whose best PGA Tour finish was a tie for eighth at last month's New Orleans Classic, was taking nothing for granted after ending the first round in control.
"I haven't been in this position before," the 37-year-old told reporters after mixing six birdies with a lone bogey at the par-three eighth where he three-putted.
"I don't feel stressed or uncomfortable in the position. I know there's tons of golf left.
"I'm just trying to keep poise about me ... just take it for what it is, enjoy it, be thankful for a good round and try to reproduce it for the next three days."
Former European No 1 Karlsson, a PGA Tour rookie this year at the age of 41, was happy to be back at the venue where he recorded his best finish on the US circuit a year ago.
"I do like the golf course," the 6-foot-5 (1.95 m) Swede said after recording five birdies and one bogey. "It's great to be back here.
"Yesterday in the practice round I learned quite quickly that you want to stay out of the rough and play the course from tee to green. I did a pretty good job of that today."
American rookie Keegan Bradley, just 11 days after winning his first PGA Tour title, charged into contention with a four-birdie 67.
"It was a good day," said the 25-year-old, who has been grouped with fellow PGA Tour rookie Jhonattan Vegas of Venezuela for the first two rounds. "I had a great pairing with Johnny. It was a really fun group out there."
Bradley was catapulted into the limelight when he clinched his maiden PGA Tour title in a playoff with compatriot Ryan Palmer at the Byron Nelson Championship two weeks ago.
Magical though that day was for him, he still has plenty of other targets to reach before the end of this season.
"Some things change but I set a group of goals before the year started and there's still a bunch I would like to achieve," said Bradley, a nephew of LPGA great and World Golf Hall of Famer Pat Bradley. "I've got plenty more work to do."
Double US Open champion Retief Goosen of South Africa opened with a 68, local favourite John Daly, previously a long-time resident in Memphis, returned a 69 and triple major winner Padraig Harrington of Ireland began with a 70.
However, Spanish former world No 2 Sergio Garcia had a day to forget as he battled to an eight-over 78 which included an ugly 11 at the par-five third where he dumped three consecutive shots into the water.
Only 32 players in the 156-strong field broke par on a difficult day for scoring.
Scores from the U.S. PGA Tour St
Jude Classic at the par-70 course on Thursday in Memphis, Tennessee.
David Mathis (US) 65
John Merrick (US) 66
Kris Blanks (US) 66
Kevin Kisner (US) 66
Robert Karlsson (Sweden) 66
Colt Knost (US) 66 Keegan Bradley (US) 67
Fabian Gomez (Argentina) 67 Jeff Quinney (US) 68
Len Mattiace (US) 68
Retief Goosen (South Africa) 68
Heath Slocum (US) 68
Boo Weekley (US) 68
Marco Dawson (US) 68
Tag Ridings (US) 68
Shaun Micheel (US) 68
Kent Jones (US) 68
Scott Gutschewski (US) 68
Martin Piller (US) 68 John Senden (Australia) 69
John Daly (US) 69
Camilo Villegas (Colombia) 69
Brendan Steele (US) 69
Carl Pettersson (Sweden) 69
Steve Marino (US) 69
Jimmy Walker (US) 69
Aron Price (Australia) 69
David Hearn (Canada) 69
Lee Westwood (Britain) 69
Stephen Ames (Canada) 69
Scott Stallings (US) 69
Bobby Hudson (US) 69 70 Michael Bradley (US) 70
Robert Allenby (Australia) 70
Troy Matteson (US) 70
John Rollins (US) 70
Dicky Pride (US) 70
Steve Flesch (US) 70
John Mallinger (US) 70
Ryuji Imada (Japan) 70
Michael Letzig (US) 70
Will Strickler (US) 70
Zack Miller (US) 70
George McNeill (US) 70
Craig Barlow (US) 70
Tom Pernice Jr. (US) 70
Bryce Molder (US) 70
Padraig Harrington (Ireland) 70
Robert Garrigus (US) 70
Yang Yong-Eun (South Korea) 70
Cameron Percy (Australia) 70
Kang Sung-Hoon (South Korea) 70
Matt McQuillan (Canada) 70
