Outages were reported in North Shore, Stanah, Thornton, Layton, Cleveleys, and Poulton, while lights flickered in South Shore, at around 8.15am.
They came amid heavy rain following 31 degree weather yesterday, which was the highest temperature recorded in the past 10 years.
Some residents said their power came back on just minutes later.
A spokeswoman for Electricity North West said a suspected lightning strike on its tower in Bispham was to blame.
She said: “Thunder storms and lightning have caused two power outages in the Blackpool area this morning.
“One outage affected 60,000 customers in the Poulton-le-Fylde, Cleveleys, Thornton and Warbreck area this morning at 8.17am.
“We managed to automatically restore power to all customers within three minutes.”
Around 200 properties in St Annes were also affected, with restoration taking longer there. By 9.50am, just 28 were still without power.
In Great Eccleston, properties were also affected by a local cable fault, Electricity North West said. It isn’t currently known how many homes and businesses are affected, but the firm hopes to restore power for most by 1.30pm.