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.

Matthew Gillard, of Connsbrook Avenue in east Belfast, pleaded not guilty to charges including kidnapping and false imprisonment.
The defendant, 25, also denied charges of common assault, assaulting a police officer and driving dangerously.
The charges relate to incidents in east Belfast and Comber on Saturday 4 April.
Newtownards Magistrates Court heard that the defendant and the woman were in his car in east Belfast when he began questioning her about who she was seeing.
A detective giving evidence in court said the woman tried to get out of the Seat Toledo car but the defendant allegedly drove off at speed, through a red light on Bloomfield Avenue.
When the car stopped on the Belfast Road in Comber, the woman escaped along a lane but was carried back to the car by the defendant, the court heard.
An off-duty police sergeant saw this and went to help the woman.
When the sergeant tried to intervene, the defendant allegedly drove his car at the officer, forcing him to get out of the way.
The sergeant was able to pull the keys from the ignition through the car's open window, but the defendant wrenched them from his grasp.
He then drove to the Grand Parade area of east Belfast where the woman was released.
He is also alleged to have sent the woman a message threatening that if she went to police about the incident he would "ruin her life in every possible way".
The court heard that the defendant handed himself over to police on Wednesday, despite being aware since Saturday that he was wanted by the PSNI.
But during police interviews he refused to answer questions put to him.
An application for bail was made but this was refused.
Mr Gillard will appear again in court on 1 May.

The energy firm reported a 24% drop in pre-tax profits for 2016 to £172m - much of that explained by the weak oil drilling and refining markets in the United States.
It reduced the valuation of its US assets by £30m, though it said there were signs of that market recovering.
Revenue fell in 2016 by 3% to £1.5bn.
Aggreko said trading conditions were particularly difficult in South America, with a renegotiation of a contract to supply power in Argentina. European trading was stronger.
The figures lacked the boost Aggreko gets regularly from supplying power to the Olympics and Winter Olympics. Comparisons with 2015 looked poorer because that year included temporary powering for the European Games.
The company pulled out of bidding for the 2016 Rio de Janeiro games, complaining that the bidding process was running too late and was disorganised.
Aggreko, which is headquartered in Glasgow with a generator assembly plant in Dumbarton, intends to cut annual costs by £25m, starting in the second half of this year.
Commenting on current trading and outlook, chief executive Chris Weston said he expected the cost cutting to help the firm achieve growth in 2017: "However, this will be more than offset by the significant impact of Argentina, and as a result we expect full year profit before tax and pre-exceptional items to be lower than last year."
As a response to the results announcement, Aggreko's share price dropped by 11%.
Mr Weston added: "Whilst the trading environment over the last 12 months has been challenging I am pleased with the progress that we are making across the group, implementing our transformation programme to return the business to growth.
"We are investing in the right technologies to reduce costs to our customers, improving our customer focus and delivering efficiencies."
The authorities in Bangladesh say power has been restored to most of the country after a nationwide blackout on Saturday.
[NEXT_CONCEPT]
A man accused of kidnapping his partner allegedly drove at a police officer who tried to save her, a court has heard.
[NEXT_CONCEPT]
Scotland-based temporary power company Aggreko has suffered a slump in its share valuation after warning of a dip in profit this year.