Officials said engineers had managed to repair plants supplying about 70% of electricity users and hoped to re-connect the rest on Sunday.
There were loud cheers in the capital, Dhaka, as lights came back in phases.
The blackout was the country's worst since a 2007 cyclone knocked out the national grid for several hours.
The authorities blamed the incident on the failure of a transmission line, which led to power plants and substations shutting down.
The high-voltage transmission line runs from Baharampur in West Bengal, India, to Bheramara in Kushtia district, in south-west Bangladesh.
The blackout began at about noon local time on Saturday and affected all parts of the country linked to the national grid.
Dhaka's hospitals and its international airport used emergency generators to continue running but many offices were forced to send employees home.
Water supplies were also badly hit as most of the pumps which lift groundwater could not function.
Bangladesh began importing electricity from India in October last year.
The authorities in Bangladesh say power has been restored to most of the country after a nationwide blackout on Saturday.