Left-handed opener Iqbal's unbeaten 103-run knock was packed with 10 fours and five sixes and he single-handedly led the Asia Cup finalists to a challenging 180 for two.
Iqbal is only Bangladeshi player, who has managed a century in all three formats of the game.
Oman's chase was shaky from the beginning and two rain suspensions only made the matter worse for them. They were 41 for 2 in seven overs when rain forced suspension of play for about 45 minutes. At resumption they were set a new target of 152 off 16 overs but only eight balls were bowled that skies opened up again.
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Jatinder Singh (25) was top-scorer for Oman while other batsmen failed miserably. Adnan Ilyas (13) was the only other batsman who managed a double-digit score. Shakib-Al-Hasan (4/15) claimed four wickets with his left-arm spin.
Bangladesh have now joined India, Pakistan, New Zealand and Australia in the 'Group of death'. They face Pakistan in their first main draw match on March 16 in Kolkata.
After a few watchful overs and losing his opening partner Saumya Sarkar (12), Iqbal combined with Sabbir Rahman (44) to punish the Oman bowlers. They added 97 runs in just 9.1 overs.
Not only the pace but the spin
Duo of 37-year-old Amir Ali and Ajay Lalcheta also troubled Bangladesh openers.
As a result, Bangladesh managed under five runs an over in the Powerplay segment. Iqbal broke the shackles with a four and six off Lalcheta but the bowler got success immediately by dismissing struggling Sarkar, who charged down the wicket, missed the line and lost his leg stump.
Sabbir supported Iqbal well with his knock, which came off just 26 balls and had five fours and six.
Brief Scores:
Bangladesh: 180 for 2 in 20 overs. (Tamim Iqbal 103 not out, Sabbir Rahman 44; Khawar Ali 1/24).
Oman: 65 for 9 in 12 overs.(Jatinder Singh 25, Adnan Ilyas 13; Shakib-Al-Hasan 4/15).