Englishman Rose, the highest-ranked player in the field, incurred a one-shot penalty when his ball moved as he prepared to tap in for par from 18 inches though he made up for that with a birdie at the par-five 18th for a 68.
Santos, with eight birdies, went one clear of Scotland's Peter Whiteford, England's Anthony Wall and Frenchman Alexandre Kaleka while six players finished on five-under.
Rose did not touch the ball with his putter and became the second high-profile player to be penalised on this year's Middle East swing after 14-times major champion Tiger Woods was handed a two-shot penalty in Abu Dhabi last week.
"I feel completely hard done by. The greens here aren't perfect - there were a lot of little ridges and humps and hollows out there. Indentations I suppose," Rose told reporters.
"It was unfortunate timing as I put my putter behind the ball which I know didn't cause it to move. But it was at the same time the ball was finding a little indentation on the green which obviously caused it to move."
Rose called the penalty on himself in the tradition of a golfer while he was watched by Manchester United players Wayne Rooney, Ryan Giggs and Paul Scholes who were taking time off from their warm-weather training camp in Qatar.
Santos, the European Tour's rookie of the year in 2012, scorched around the Doha Golf Club layout in the calm morning conditions with the usual winds only picking up later in the day.
"Winning Rookie of the Year gave me a lot of confidence for this season," said Santos, who finished fourth last week in Abu Dhabi.
"I practice a lot to have a more consistent game and that's my target for this season, that and just enjoy myself."
World number five Louis Oosthuizen, paired with Rose for the first first two rounds and Ryder Cup player Martin Kaymer, double-bogeyed the last hole for a 71.
German Kaymer, the 2010 U.S. PGA Championship winner, holed out with his second shot on the fourth for an eagle but also had trouble on 18 with a bogey as he signed for the same score as Rose.
American world number 11 Jason Dufner, who is considering taking up European Tour membership to help improve his all-round game, also carded a 71.
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