McLaughlin set an early benchmark in the Fast Six pole shootout on alternates at 1m06.329s and ran a second lap on this set – but made a tiny error at Turn 5 – before switching to his second set.
Power went earlier to his second set of alternates and lowered the bar to 1m06.046s with a minute to go, but then it was his turn to run wide at Turn 5.
However McLaughlin wasn’t to be denied with 1m05.949s on his final effort to snatch pole, the 300th for his team owner Roger Penske.
Rahal Letterman Lanigan Racing driver Lundgaard jumped up to third on 1m06.081s, ahead of Pato O’Ward (Arrow McLaren) and Felix Rosenqvist (Meyer Shank Racing).
Marcus Armstrong, in his first-ever Fast Six appearance for Chip Ganassi Racing, completed the top six.
Lundgaard had earlier set the benchmark in the Top 12 qualifying session that set the Fast Six contenders, logging a 1m05.813s on alternates before aborting an even quicker lap to save his rubber.
Power was just 0.063s slower in second, ahead of McLaughlin, Armstrong, O’Ward and Rosenqvist.
Graham Rahal (RLL) narrowly missed out on joining Lundgaard in the fight for pole and will line up seventh, alongside Josef Newgarden (Penske).
Kyle Kirkwood (Andretti Global), a mystified Alex Palou, Romain Grosjean (Juncos Hollinger Racing) and Tom Blomqvist (MSR) also fell at this stage.
Palou had topped his first qualifying group before losing pace in the Top 12 session, having posted a best lap of 1m05.5862s to best O'Ward, Armstrong, Rahal, Grosjean and Kirkwood.
Long Beach GP winner Scott Dixon (CGR) was only seventh in his group and missed out, along with Colton Herta (Andretti), Santino Ferrucci (AJ Foyt Racing), Linus Lundqvist (CGR), debutant Luca Ghiotto (Dale Coyne Racing), Kyffin Simpson (CGR) and Sting Ray Robb (Foyt).
After setting the pace in second practice, qualifying was a disappointment for Rinus VeeKay (Ed Carpenter Racing). He reported “no power” over the radio on his opening run and the Dutchman's electrical issue could not be fixed in time to run again.
McLaughlin set the pace with a lap of 1m05.814s, a couple of tenths ahead of team-mates Power and Newgarden, who saved a big moment at the exit of the final turn on his penultimate lap. Lundgaard was fourth, ahead of Rosenqvist and Blomqvist.
Joining VeeKay in missing out were Christian Rasmussen (ECR), Alexander Rossi (McLaren), Marcus Ericsson (Andretti), Agustin Canapino (JHR), Jack Harvey (Coyne), Theo Pourchaire (McLaren) and Pietro Fittipaldi (RLL).