The 28-year-old American hasn't managed a top-10 showing since sharing second in November at Dubai.
The 29-year-old Northern Irishman overcame a shaky start at TPC Sawgrass to card six birdies against two bogeys and a double-bogey.
Ian Poulter (66), Jim Furyk (64), Brian Harman (69) and Abraham Ancer (66) are tied for third at nine-under 135.
South Korea's Jinho Choi fires a brilliant eight under par 64 to finish joint second in a nine-way tie, which is a European Tour record.
Nick Cullen, Nacho Elvira, Mike Lorenzo-Vera and Erik Van Rooyen are just a stroke behind.
Australia’s Deyen Lawson fires his second hole-in-one of the season.
The Spaniard will head into the second round two clear of Keegan Bradley, who shot a flawless five-under-par 67 to take sole occupancy of second place on the leaderboard
Qatar’s Saleh Al Kaabi, Jaham Al kuwari and Qatar Open winner Mikkel Mathiesen all struggled in windy conditions.
With 144 players blending an intriguing mix of youth and experience, this year’s edition is set to be another memorable addition to the tournament’s storied history.
Thomas Pieters, Kurt Kitayama, Fabrizio Zanotti and Wilco Nienaber are all set to make their mark in the Qatari capital.
In a post on Twitter, Woods said the problem was unrelated to the lower back issues which sidelined him for nearly two years, and added he had no concern over his long-term fitness.
The 34-year-old replaced Englishman Rose by a narrow margin.
The quality of golf in Qatar continues to go from strength to strength with the support of the Qatar Golf Association’s Junior Programme sponsored by Qatar Gas.
The 43-year-old has played in all except two editions of the event and has a stellar record
The 21-year-old rookie fired a final round four-under 68 to finish on 21 under and two strokes clear of fellow Australian Ashley Hall and New Zealand's Josh Geary at the Millbrook Resort course.