A late acceleration saw the US 60m indoor champion power his way to a new personal best 9.93sec with France's Jimmy Vicaut second in 10.02 and Italy's Filippo Tortu snatching third place in 10.04.
"I felt really great, everything fell into place," said 24-year-old Baker.
"Overall it was very fluid. Last year I came third here and to follow on from Eugene with a personal best is super."
It was world silver medallist Coleman's second defeat in a week to Baker as the fight for men's 100m supremacy in the post-Usain Bolt era continued in the fourth leg of the Diamond League.
Olympic champion Brianna McNeal crashed in the women's 100m hurdles after her wins in Doha and Shanghai.
McNeal finished last in the nine-athlete field with fellow American Sharika Nelvis taking gold to complete her set after silver in Shanghai and bronze in Doha.
Nelvis clocked 12.76 with Jamaica's Danielle Williams second in 12.82.
McNeal trailed home in 15.80.
Kenya reigned supreme in the middle distance events completing podium sweeps in both the men's 800m and the women's 3,000m steeplechase, and going 1-2 in the men's 1500m and steeplechase.
Commonwealth champion Wycliffe Kinyamal led home Ferguson Cheruiyot in the men's 800m followed by countryman Jonathan Kitilit with all three under the 1min 45sec mark.
In the women's steeplechase US world champion Emma Coburn started strong leading her rivals but fell allowing Kenyan trio of Hyvin Kiyeng, Celliphine Chepteek Chespol and Norah Jeruto to race to the top three spots respectively.
"Had I not fallen I would have won," said Coburn who trailed in fourth. "It was just a back luck day."
"I feel good about my win even more as this is my first race of the season," said former world champion Kiyeng.
In the men's 1,500m Timothy Cheruiyot led fellow Kenyan Elijah Motonei Manangoi with Ethopia's Samuel Tefera in third.
Conseslus Kipruto won the men's 3,000m steeplechase in a world lead time of 8.10.08 with fellow Kenyan Benjamin Kigen second.
American world pole vault champion Sam Kendricks claimed back-to-back wins after Eugene with a season's best 5.84 metres.
Qatar's Abderrahaman Samba set a blistering time in the men's 400m hurdles to set a new Diamond League record.
Samba, winner of the Doha meet, clocked 47.48 to leave Norway's world champion Karsten Warholm trailing second in 47.82.
America's Georganne Moline spoilt set a scorching pace for a season's best 53.97sec in the women's 400m hurdles.
"Finally I am in the race for the diamonds!" said Moline after recapturing the event she won back in 2015.
She spoilt Janieve Russell's bid for a third Rome title with the Jamaican, who won in Eugene last week, second in 54.08.
Olympic champion Dalilah Muhammad was third in 54.65.
World 100m and 200m women's silver medallist Marie-Josee Ta Lou moved up from the 100m win in Eugene, winning the 200m with as season's best 22.49sec.
Commonwealth champion Fedrick Dacres of Jamaica was the surprise winner of the men's discus with a throw of 68.51 metres.
The 24-year-old from Kingston left Lithuania's world champion Andrius Gudzius trailing in second with 68.17.
Germany's Robert Harting, the 2012 Olympic champion, was fifth best, with four-time Diamond Trophy winner Piotr Malachowski of Poland ninth.
Croatia's two-time world and Olympic champion Sandra Perkovic won the women's discus for the 40th Diamond League victory of her career and third here in Rome.
Perkovic pulled out a meet record throw of 68.93 metres.
"I'm proud to be the most successful athlete in Diamond League history," added Perkovic, 27, who remains on track to win the Diamond League title in her discipline for the seventh year.
South Africa's Luvo Manyonga won a battle in the men's long jump with 8.58metres to edge out Cuba's Juan Miguel Echevarria 8.53.