The left-hander scored 138 and was associated in a record stand with captain Habibul Bashar (76) that helped the home side reach 355-5 at stumps on the opening day of the first Test on Sunday.
Rajin Saleh (35) and Khaled Mashud (two) were the not out batsmen, with Bangladesh looking determined to inflate the total further on a pitch expected to help spinners as the match progresses.
The bowling attack of pacemen Brett Lee, Jason Gillespie and Stuart Clark and leg-spinners Shane Warne and Stuart MacGill were left frustrated against a side which has in the past struggled to bat a full day in Tests.
Bangladesh have lost both their previous Tests to Australia by innings margins.
But taking inspiration from their shock victory over Australia in a tri-series one-dayer in England last year, the home side took the bull by the horns and played aggressively after electing to bat.
Nafees led the charge with a well-paced knock that was the third-highest individual effort for Bangladesh, during which he drove and cut the pacemen with ease and swept the spinners at will.
Nafees, whose previous best in four Tests was 51, struck 19 fours during his 189-ball knock and got to his century with a four to fine-leg off Warne.
The 20-year-old added 187 for the second wicket with Bashar, which broke the previous Bangladeshi record of 167 for any wicket -- between Bashar and Javed Omar against Pakistan at Peshawar in 2003.
Bashar attacked Warne often and helped himself to 11 fours off 113 balls, consolidating the home side's position after they raced to 144-1 by lunch.
Nafees was dropped on 66 by Warne at the lone wide slip off paceman Gillespie in the second session.
He then put his head down once again to frustrate the bowlers till he was bowled from behind the legs by MacGill while sweeping.
"It is a great feeling to score your first century against the world's best team," Nafees said. "It also feels good when you realize that your runs have gone a long way in the team's cause."
Bashar was earlier out on the stroke of tea when he tried to pull MacGill but gave a catch to Lee at mid-on. MacGill, who also dismissed Aftab Ahmed, was the pick of the bowlers with 3-82.
"Our partnership was a very important one. Nafees batted superbly and made batting today look very easy but it wasn't really so," said Bashar.
Visiting captain Ricky Ponting led his side to a fine 3-0 Test series triumph in South Africa before embarking on their maiden full tour of this country. But he was short of ideas against the free-stroking Bangladeshis.
The home side reached 200 in the 44th over after sprinting to 100 in just the 20th over, with Nafees playing fine shots all around the ground and Bashar joining him in the run feast.
Nafees had earlier put on 51 with opener Omar (27), who was trapped leg-before by Gillespie.
Omar struck six fours including two consecutive ones down the leg side off new-ball bowler Stuart Clark.
The second and final Test will be held in Chittagong from April 16.