Sagstrom carded a four-under-par 68 in beautiful conditions at Samanah Golf Club in Marrakech for a 90-hole score of 343, 17-under-par, to win from Valdis Thora Jonsdottir of Iceland.
Boutier, who had either led outright or held a share of the lead for the first four rounds, ended with a 75 to tie for third place on 14-under-par with Karolin Lampert of Germany, Agathe Sauzon of France and Australian teenager Celina Yuan.
Thirty players from 14 different countries qualified for category 8 membership of the LET, with the mark falling at two-under-par.
Two English amateurs, Inci Mehmet and Lauren Horsford, were among those to secure a card.
Winning Ryder Cup captain Paul McGinley believes Tiger Woods has his work cut out to get back to winning ways.
“It’s not sacrilege when people say that golf needs Tiger back – it’s showbiz,” said McGinley as he reflected on the world No 1’s comeback earlier this month after a 15-month absence.
“He’s still the number one draw, and that showed in the TV ratings when he came back. Personally, I think the reaction to the way he played in the Hero World Challenge was over the top.
“He has further to jump if he is to get back to the top level, where he was, and can he do it at 41 years old?
“Nobody has ever done it before at his age – there have been sporadic performances, like Jack Nicklaus winning the Masters at 46, but it’s not as if he was dominating the game then.
“Tiger’s a little bit like a footballer who reaches 32: He can still play the odd great game, as Steven Gerrard did at Liverpool, but can he do it day after day? That’s the big hurdle.
“The new generation of players who can hit longer than him are simply not afraid of Tiger any more. These guys want a piece of him, they want to go head-to-head with him.
“I’m not sold on his comeback – I just don’t see him dominating in the way he once did.”
Graeme McDowell will make a return to the Commercial Bank Qatar Masters when the Northern Irishman competes in the tournament’s landmark 20th edition at Doha Golf Club next month.
The 37-year-old will be competing in Doha for the first time since 2012, when he made his sixth appearance in a decade since making his tournament debut as a 23 year old in 2003. His best result remains a share of fourth in 2007, when he finished three strokes behind two-time US Open champion Retief Goosen.
“I’m looking forward to returning to Doha for the 20th Commercial Bank Qatar Masters as it has been a few years since I’ve played there and I have fond memories of the tournament,” said McDowell.
Geoffrey Marks, who led Great Britain & Ireland to a first Walker Cup win on US soil, has passed away at the age of 78.
The Englishman played twice in the amateur event himself - in 1969 and 1971 - before masterminding an historic 12.5-11.5 victory at Peachtree in 1989.
In 2008, Marks was made an OBE in the Queen’s Birthday honours list for his services to golf.
“He was a talented golfer and one of only two GB&I Walker Cup captains to experience victory in the United States,” said R&A secretary Martin Slumbers in paying tribute to Marks.
“For many years, he played a key role in setting the hole locations for The Open Championship and served on several of our committees.
“He made a substantial contribution to golf and he will be missed by many in the game.”