The brief outages occurred shortly before 5:20 p.m. Monday, minutes before the game between the 49ers and the Pittsburgh Steelers was set to start, and again at about 6:45 p.m. during the second quarter.
In Lee's letter, addressed to 49ers president Jed York, he wrote that the second outage was caused by "a malfunctioning switch on the backup power system inside the stadium."
He said city crews would be replacing the switch starting today, and expect to complete the work next Wednesday.
Lee, who called the outages "a national embarrassment" on Tuesday, wrote in the letter that the city is also installing additional backup power to the computer that controls the power systems inside the stadium, a project expected to be completed today.
PG&E chief executive officer Anthony Earley sent a separate letter to the 49ers on Thursday admitting fault for the first outage, which was caused when a splice, which connects two overhead electrical wires, failed and the power line fell to the ground on Ingerson Avenue near the stadium.
The stadium's backup electrical feed switched on, but the metal halide stadium lights took several minutes to cycle back on, Earley wrote.
"No one expected that those lights would go out or that they would briefly take center stage on Monday," he wrote.
PG&E spokeswoman Katie Romans said the utility has since replaced the failed splice, as well as six others in the area as part of "an active investigation into all of our surrounding infrastructure."
Earley wrote in the letter that PG&E is also performing a failure analysis at its lab in San Ramon to determine what caused the splice to fail. The 49ers won Monday's game 20-3 over the Steelers, improving their record to 11-3 on the season.
The team, which clinched a playoff spot earlier this month, plays on the road for the final two weeks of the regular season, but is assured of at least one home playoff game in January.
Earley wrote, "PG&E will continue to partner with the City and County of San Francisco to improve electric reliability throughout the City and at Candlestick Park as the 49ers prepare to host what we hope will be multiple playoff games."