Perera returned career-best figures of 3-23 and Maharoof bagged 3-30 against a team that failed to settle down on the easy-paced wicket at the Shaheed Chandu stadium here on Monday.
Former skipper Khaled Mahmud was the only batsman to offer resistance, making 36 in his last international appearance.
Only two other batsmen, Aftab Ahmed (21) and Alok Kapali (19 not out), reached double-figures to leave home fans at the new international venue disappointed.
Bangladesh, who have lost all their 14 previous One-dayers against Sri Lanka, were rattled by Maharoof and Perera with the new ball.
Maharoof had opener Shahriar Nafees and Mohammad Ashraful caught behind and trapped Rajin Saleh leg-before with one that came in sharply.
Ahmed jumped out and missed the line of the ball to give the first wicket to Perara who then dismissed Khaled Mashud as Bangladesh were reduced to 37-5 and in danger of falling below their lowest total of 76.
Dilhara Fernando removed captain Habibul Bashar to make it 51-6 before Mahmud and veteran Mohammad Rafique figured in a 31-run stand for the seventh wicket.
Perera later came on to dismiss tail-ender Mashrafe Mortaza (six) to better his previous best of 3-55 on debut against England in 1999.
Fernando and left-arm spinner Sanath Jayasuriya finished with two wickets each.
Sri Lanka, who earlier this month made the finals of a tri-series in Australia also featuring South Africa, rested ace spinner Muttiah Muralitharan, seamer Chaminda Vaas and all-rounder Russel Arnold for the One-dayers.
The second match will be played here on Wednesday and the final One-dayer will be held in Chittagong on Saturday. The One-day series will be followed by Tests in Chittagong and Bogra.