The opener, who had told the team coach he would hit a tonne, became the first Bangladesh player to score a hundred in a Twenty20 International as his side proved they are too good to jostle with associate nations to qualify for the Super 10 stage.
Put into bat, Bangladesh posted an imposing 180-2, which proved too much for Oman's limited batting resources as the associate nation, chasing a revised 120-run victory target in 12 overs, managed 65-9 to lose via the Duckworth-Lewis method.
The victory sees Bangladesh join India, Australia, New Zealand and Pakistan in Group Two of the Super 10 stage.
Bangladesh got off to a slow start, especially with Soumya Sarkar (12) struggling to middle the ball throughout his 22-ball stay in the middle.
Tamim's wide range of strokes, which he underlined with 10 fours and five sixes, meant the southpaw (103 not out), who turns 27 later this month, could not be tamed.
Tamim's aggression saw him race to fifty off 35 balls and he and Sabbir Rahman (44) plundered 97 runs in nine overs to lay the foundation for a big total.
Tamim took 60 balls to reach his century, bringing up the milestone with a boundary off Bilal Khan before leaping in joy and gesturing to coach Chandika Hathurusingha.
"We were having this camp back home when Chandi asked for a hundred," Tamim said at the innings break. "I put my hands up and said, 'I will give you a hundred in this World Cup'. It feels good that I kept my promise."
Oman stuttered early in their chase, which saw two rain interruptions before Bangladesh completed a clinical victory.
Netherlands beat Ireland by 12 runs in the earlier qualifier, which was reduced to a six-overs-a-side contest following incessant rain in the north Indian city.
(Reporting by Amlan Chakraborty in New Delhi; editing by Ken Ferris)
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