The 23-year-old clocked his sixth sub-10 second time of the season as he came home in 9.99, ahead of Asafa Powell.
Gatlin was fourth in 10.14, behind Femi Ogunode (10.13) and ahead of De Grasse, who was fifth in 10.21.
Jamaica's Olympic champion Elaine Thompson beat the Netherlands' Dafne Schippers in the 200m.
The pair were separated by only a tenth of a second in last year's Olympic final, and Thompson triumphed in Doha by 0.26 seconds in a time of 22.19.
Britain's Robbie Grabarz, who took silver in the European Indoors in March, claimed second place in the high jump, clearing 2.31m in his first outdoor event of the season.
Olympic champion Caster Semenya claimed a commanding victory in the 800m, coming home in a world-leading time of one minute 56.61 seconds.
Burundi's Francine Niyonsaba, who won silver behind the South African in Rio, was the only other woman to better that time in the whole of 2016.
Ethiopia's Genzebe Dibaba - who broke a 22-year-old 1500m world record in 2015 and won silver over the distance in Rio - was fifth in her first 800m outing.
Olympic champion Thomas Rohler threw 93.90m to win the javelin competition by more than four metres.
The German's throw moves him to second in the all-time list, with only Czech great Jan Zelezny having thrown further.
Desiree Henry was well short of the 22.69 she clocked earlier this year in California as the 21-year-old finished seventh in the 200m.
Holly Bradshaw, who missed the indoor season with injury, finished fourth in the pole vault with a best of 4.55m.
Cindy Ofili finished down in seventh as American world record-holder Kendra Harrison won the 100m hurdles in 12.59, while Andrew Butchart came eighth in the 3,000m and Chris Baker finished seventh in the high jump.

The 28-year-old joined the U's from Rotherham United in February of 2016 after an initial six-week loan spell.
Maguire, who has played for Scotland twice, scored 17 goals in 54 appearances for Oxford last season.
"He had many offers to consider so we are delighted he has chosen us," boss Lee Clark told the club website.
Find all the latest football transfers on our dedicated page.
South Africa's Akani Simbine continued his impressive start to 2017 by beating Justin Gatlin and Andre de Grasse in the 100m at the Doha Diamond League.
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Bury have signed Scotland international striker Chris Maguire from fellow League One side Oxford United on a two-year contract.