The company said Lancaster's Caton Road substation went offline at 11:00 BST, leaving parts of the city and nearby Morecambe and Carnforth without power.
Power supplies resumed at 16:30 BST in the remaining 10,000 properties after 53,000 had theirs restored earlier.
The firm said it was not yet known what caused the outage and thanked customers for their "support".
A flood at the facility during Storm Desmond in 2015 left 55,000 without power.
The outage resulted in travel problems, with many traffic lights not working, and caused disruption to schools, universities and businesses.
Lancaster town hall closed while the outage was dealt with. It later reopened but Lancaster City Council tweeted it "can only deal with basic enquiries".
Salt Ayre Leisure Centre in Lancaster was closed and it only accepted cash payments when it reopened.
Lancaster University was affected and tweeted wi-fi is available outside the chaplaincy centre, security lodge and information systems services.
The university's student union sent a tweet telling students who were facing exams to turn up as usual.
St John's Hospice and Lancaster Cathedral both tweeted that power had returned.

Officers were contacted with reports of a man seen in Colchester, thought to resemble one of the offenders involved in the attempted abduction in Norfolk.
A victim was threatened with a knife by two men who tried to force him into a car near the Norfolk base last week.
Police investigating the incident at RAF Marham confirmed the sighting was not one of the suspects.
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The Norfolk force issued an e-fit earlier this week in an attempt to track down the two men, who fled the scene in a dark-coloured people carrier, which the police are still trying to trace.
A Ministry of Defence spokesman said safety of personnel was "paramount".

A team of the Anti-Drug Smuggling Unit searched the 27-year-old's home in Port Louis and found 22 doses of heroin and a further one gram of the drug.
Equipment used in the preparation and packaging of heroin, including razor blades and scales, were also seized.
Leopold is the first-choice goalkeeper for Mauritius Professional Football League champions team ASPL 2000.
He was also the reserve goalkeeper for the national team during the last Africa Cup of Nations qualifying campaign.
Leopold helped ASPL 2000 to win the Charity Shield on Saturday on Rodrigues Island where they beat Pamplemousses SC 1-0.
As the news of his arrest broke, some people gathered outside Leopold's home to prevent the ADSU from taking him to police custody.
According to information gathered by the BBC, the police had been tracking Leopard closely for some time and gathering intelligence.
A provisional charge of drug dealing has been lodged against him.
Both the Mauritius Football Association and ASPL 2000 refused to comment on the issue.

The addition of Permian, who was successful in the Dante Stakes at York, and last week's Goodwood winner Khalidi, means the total purse for the Classic on 3 June will be £1.625m.
The John Gosden-trained Cracksman is the favourite.
Cracksman beat Permian in the Derby Trial in April.
Meanwhile, trainer John Jenkins has defended his owner's decision to run 1,000-1 outsider Diore Lia, where she will be ridden by apprentice Gina Mangan.
Diore Lia has made just two competitive appearances to date, beating only one rival on her Epsom debut late last month before finishing down the field at Lingfield.
Owner-breeder Richard Aylward is keen to let his filly take her chance to generate publicity and funds for Great Ormond Street Children's Hospital.
"If I didn't run her, someone else would. The owner is keen to run her and has set up a charity. He's there for the big day," said Jenkins.
"I had a runner in the Derby a long time ago. That was an outsider as well and it didn't finish last.
"Has there ever been a 1,000-1 winner of the Derby?"

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27 October 2014 Last updated at 07:50 GMT
It was held earlier this month in Hunan province, in a mountain range thought to have inspired the floating mountains of Pandora in the Hollywood blockbuster film Avatar.
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An estimated 63,000 properties in north Lancashire were hit by a power cut, Electricity North West has said.
[NEXT_CONCEPT]
A sighting of a man near a barracks is not linked to an investigation into a kidnap bid at RAF Marham, police said.
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Mauritius international goalkeeper Joseph Kinsley Steward Leopold has been arrested for drug dealing.
[NEXT_CONCEPT]
The 2017 Derby at Epsom will be the richest race ever staged in Britain after two horses were added as late entries at a cost of £85,000 each.
[NEXT_CONCEPT]
It might not seem like your idea of fun but dressing like a bat and jumping off the side of a cliff is exactly what a group of wingsuit base jumpers have been doing in China, as part of a downhill sky race.