Agha hit 106 off 98 balls, but his dismissal in the 48th over saw Pakistan eventually bowled out for 279 on Sunday with skipper Shaheen Shah Afridi stumped off the final ball of the doomed chase.
Opening batter Tanzid Hasan's (107) first ODI hundred had earlier propelled Bangladesh to 5-290 after Afridi won the toss and elected to field on the same wicket where Pakistan were bowled out for just 114 in the first game which Bangladesh won by eight wickets.
Bangladesh lost the second ODI by 128 runs under the DLS Method when they were also dismissed for 114.
"Definitely (it) was an excellent match," Bangladesh captain Mehidy Hasan Miraz said.
"It was an excellent wicket and if we got 300 it would be better, but we are playing well, especially the way Tanzid batted."
A revamped Pakistan, who awarded six ODI debuts in the series, struggled to cope with the pace of Taskin Ahmed (4-49) and Nahid Rana (2-62), and slipped to 3-17 after three overs.
Ghazi Ghori (29) and Abdul Samad (34), two of the six Pakistan debutants in the series, revived the chase with a 50-run stand before Pakistan slipped to 5-82 in the 18th over.
But Agha brought Pakistan back into the hunt with a 79-run stand with Saad Masood (38) and added 52 runs with Afridi for the eighth wicket. Agha completed his third ODI hundred off 89 balls with nine fours and four sixes.
With 28 needed off the final two overs, Afridi smacked Mustafizur Rahman (3-54) for two big sixes in the penultimate over and Rishad Hossain had Afridi stumped to complete a memorable series win for Bangladesh.
The opening pair of Tanzid and Saif Hassan (36) had earlier provided the hosts with a solid start of 105 runs on a worn wicket.
Tanzid raised his hundred off 98 balls with seven sixes and six fours and Towhid Hridoy lifted Bangladesh to a fighting total in the last 10 overs with an unbeaten 48 off 44 balls.
"We gave chances to youngsters and fought till the last ball," Afridi said.
"Really proud of the way they played and we will support them."
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