Pulisic put the U.S. in front minutes after coming off the bench with a glancing header and McKennie struck from close range shortly before full-time to give the Americans a third straight win over CONCACAF rivals Mexico.
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The U.S., who are now in first in the CONCACAF qualifying standings thanks to a superior goal difference, downed Mexico 3-2 in the Nations League final last June and beat El Tri 1-0 at the Gold Cup decider two months later in the teams' previous two meetings.
"It was incredible, and the fans made it all that much better," Pulisic said of the sold-out Ohio crowd, who were undeterred by the cold and wet conditions.
"They really came out tonight. It was so loud in there. Moments like that is what we live for."
An entertaining, end-to-end opening 20 minutes saw both keepers called into action, with Zack Steffen keeping out a low drive from Hirving Lozano and Guillermo Ochoa smothering a shot from distance by the Americans' Tim Weah.
The frenetic pace did not slow as the first half wore on, but neither Mexico nor the U.S. could find the back of the net as the teams went into the break locked in a 0-0 draw.
McKennie forced a save from Ochoa in a lively start to the second half for the home team, smashing the ball on frame after Weah picked him out at the top of the penalty area with a nice cutback pass.
McKennie, Steffen and Mexico's Luis Rodriguez were all shown yellow cards after a dustup involving Brenden Aaronson. The caution for McKennie means he will miss the U.S. match against Jamaica on Tuesday due to yellow card accrual.
With the U.S. chasing a goal, Gregg Berhalter brought on Pulisic minutes later for Aaronson as the Chelsea player made his first appearance for the Americans since leaving a September match against Honduras with an ankle injury.
The move paid off brilliantly for the U.S. as Pulisic rose to meet a pinpoint cross from Weah just inside the six-yard box and headed past Ochoa to give the hosts a 1-0 lead.
Some nice interplay from the U.S. led to its second goal when the ball fell to McKennie inside the penalty area and he made no mistake with only Ochoa to beat to double the lead.
Pulisic said fans should always expect sparks to fly when the adversaries square off.
"USA and Mexico, you know what you're going to get. Intensity," he said.
"It was a crazy game for sure but it's what we expected. It was tough to break them down. I'm happy I could come in and help us out. In the end, that's three huge points."
After the match, Mexico manager Gerardo "Tata" Martino admitted it was a tough defeat, but said his team remained focused on World Cup qualification.
"We are playing in World Cup qualifying, this isn't a personal head-to-head against the United States," Martino said. "I understand the importance of this game and the rivalry and having three consecutive defeats against an opponent that all Mexicans always want to beat.
"We have to focus on finding a way to regain our form in the qualifying."
Miles Robinson was shown a second yellow card late on, leaving the U.S. to finish the match with 10 men. The Atlanta United defender will also be unavailable against Jamaica.
The U.S. has 14 points from seven games at the halfway point of CONCACAF's Octagonal World Cup qualifying process, level on points with Mexico but ahead on goal difference.