Fir Park and neighbouring properties were affected by the power cut about 15 minutes before kick-off.
Kick-off was delayed by 10 minutes but the home club confirmed they had taken the decision to postpone the match for safety reasons.
A Fir Park game against Hibernian was abandoned at half-time after a floodlight fire in December last year, but this time the problem was outside the Lanarkshire club's control.
Although some smoke was visible coming from the area between the Davie Cooper Stand and Phil O'Donnell Stand after the electricity first failed, this was as a result of the club's diesel-powered back-up generator automatically kicking in.
Power was restored before 4pm but that was ahead of schedule according to the advice the club received.
Motherwell chief executive Leeann Dempster said: "We called ScottishPower who informed us there was a major outage in North Lanarkshire and very early indications were that there would be some power back by 6pm.
"At that stage it's a fairly easy decision because the generators are supposed to run our emergency lighting to get people out, and you can't run a football match if you have no power in hospitality areas and toilets etc.
"We took 10 minutes to get match abandoned tickets in place so supporters can either come to the next game or have their money back and then we made the announcement.
"Most people think we don't know how to run a game here because it has happened twice but this is outwith our control."
Dempster added: "Some people are a bit annoyed and understandably. But what do we do, run a match and something happens and people will say 'why did you not evacuate it when you didn't have any power?' It's a no-brainer unfortunately."
Dempster estimated that the postponement would cost the club up to £40,000.
She added: "We just have to take it on the chin, supporters and hospitality customers are going home disappointed but what we don't want to do is infuriate them further by not looking when they come back again.
"I believe that Wishaw General is out so there are major issues in North Lanarkshire.
"When we don't have a football match compared with what is happening in Wishaw is irrelevant almost."
SPL match delegate Willie McDougall praised the home club for their response.
"The whole co-ordination of an emergency situation has worked out well," he said. "The right decision was made on safety grounds.
"Fans will probably be saying 'it's daylight, why can't we play football?', but when you have a crowd and there's a responsibility for safety, that's the name of the game."
Both managers were naturally disappointed but philosophical about the postponement.
Motherwell manager Stuart McCall said: "There is nothing we can do about it. The worst thing is we have to wait two weeks for the next game."
His United counterpart Peter Houston added: "First and foremost there is no-one to blame here, certainly not Motherwell Football Club."
A spokesman for ScottishPower said the power failure was caused by a fault in one of its underground cables in the Motherwell area at about 2.50pm and that about 250 properties were affected.
"Everyone was reconnected within one hour," the spokesman said. "We apologise for any inconvenience this has caused."
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