Power grabbed his 68th career pole with Andretti watching from pit lane Saturday at Laguna Seca Raceway. Andretti made his way to Power's car and gave him a thumbs-up, while Team Penske teammate Scott McLaughlin hopped on the side of Power's car to give him a high-five.
"Didn't even occur to me until they told me. I can't celebrate so much because I've got to be ready for [the finale]," said Power, who won his fifth pole of the season to break the mark.
Andretti eventually made his way to the staging area where the Australian was being celebrated for the pole-winning run.
"I tell you, to see Mario Andretti walk up the pits and shake his hand, that's something I'll remember," said Roger Penske, owner of Power's car.
Andretti, who was also passed this year for second on the wins list by Scott Dixon, was pleased for Power.
"I know how much I love qualifying and he's the same," Andretti said. "It was coming. It's beautiful. It's great for the sport, and records are meant to be broken."
Power, who was given a new hat that read "68 poles," said the scene on pit lane with Penske and Andretti was "surreal."
"At such a crucial point, I couldn't celebrate it very much and I don't want to give out too much energy because I need to save it," Power said. "When you have those sort of figures there congratulating you, you are sort of pinching yourself."
The pole-winning run gave Power one additional point in the standings. The current IndyCar leader heads into Sunday's finale up 21 points over both Team Penske teammate Josef Newgarden and six-time IndyCar champion Scott Dixon. Indianapolis 500 winner Marcus Ericsson is 40 points out and McLaughlin trails by 42 in what remains the closest IndyCar championship race since 2003.
It was a fairly disastrous qualifying session for all the championship contenders besides Power.
The session fell apart almost instantly when Newgarden, a two-time IndyCar champion and winner of a series-high five races this season, went off course in the corkscrew and found himself stuck in the gravel. He was penalized his two fastest laps, was not permitted to advance out of the first group and will start 25th on Sunday.
"I just made a mistake. It's frustrating," Newgarden said. "I think we have the fastest car in the field. But it's a bummer, it's a bummer for everybody. It's not over, but it's not ideal what just happened."
IndyCar extended the session to give the qualifiers a chance to complete one lap, but Dixon failed to advance and will start 13th. McLaughlin and Ericsson advanced, but Ericsson spun in the second group and qualified 10th, two spots behind McLaughlin.
It made for a Fast Six final shootout that included Power, the Andretti Autosport pairing of Alexander Rossi and Romain Grosjean, as well as outgoing IndyCar champion Alex Palou and Pato O'Ward of Arrow McLaren SP and rookie Callum Ilott.
Power had no trouble and nipped Ilott by 0.0193 seconds in Ilott's best career qualifying effort.
Rossi qualified third and was followed by Grosjean, Palou and O'Ward.
Colton Herta, the two-time defending race winner from pole, went off course and qualified 18th. It's possible that Sunday marks Herta's final IndyCar start as the 22-year-old Californian is being courted by AlphaTauri in Formula One.