Chelsea star Pulisic nodded home a 74th-minute cross from Timothy Weah just five minutes after coming on as a second-half substitute to put the Americans 1-0 up in Cincinnati.
Juventus's McKennie then made the game safe five minutes from time, sweeping a low finish past Mexico goalkeeper Guillermo Ochoa after Weah's deflected low cross caused confusion in the Mexican area.
A late red card for Miles Robinson after a second bookable offence left the US down to 10 men for the closing stages, but US coach Gregg Berhalter's young side were not to be denied.
The win leaves the United States on top of the eight-team final round of CONCACAF standings with 14 points from seven games.
The top three finishers in the standings qualify automatically for next year's finals in Qatar, while the fourth place team advances to an inter-continental playoff.
Friday's win means the US are firmly on course to exorcise the ghost of their 2018 World Cup qualifying debacle, when they failed to reach the finals in a devastating blow for US football.
It also completed a clean sweep of victories by the US over Mexico in 2021 following wins over 'El Tri' in the CONCACAF Nations League final and Gold Cup final.
"It was incredible, the fans really came out tonight and moments like that are what we live for," US goalscorer Pulisic said.
- 'A crazy game' -
"US-Mexico you know what you're going to get - it was a crazy game for sure, that's what we expected. They were tough to break down and I'm happy I could come in and help us out.
"We're happy with where we are now. We've got a lot of games left to play and this is just one step closer to get us to the World Cup."
The US had struggled to get a foothold in the game during an error-strewn first-half performance, and had Manchester City reserve goalkeeper Zack Steffen to thank for two crucial saves to deny Mexico.
Steffen rescued the US in the 12th minute, diving to his right to turn a goal-bound Edson Alvarez shot from the edge of the area around the post.
Steffen then pulled off another fine save after Alvarez's clever through-ball released Hirving Lozano. Lozano looked certain to score but Steffen spread himself to snuff out the danger.
Those were the best Mexican chances of the game, and the US came out in the second half looking far more threatening.
McKennie almost opened the scoring on 49 minutes but saw his shot tipped over by Ochoa, and Ricardo Pepi should have done better on 54 minutes but scooped his shot over the bar.
The growing US pressure told soon after Pulisic's introduction, the forward heading home Weah's cross to make it 1-0, sparking wild celebrations among the home crowd.
In other games on Friday, Canada boosted their chances of a first World Cup appearance since 1986 after a 1-0 win over Costa Rica in Edmonton.
Jonathan David's 57th-minute goal sealed a win which leaves Canada in third place in the table with 13 points, just one off the lead.
Panama, bidding to repeat their 2018 World Cup appearance, also reignited their challenge with an improbable 3-2 away win over Honduras.
Honduras looked to be cruising to victory after goals from Alberth Elis and Brayan Moya left them 2-0 up with 13 minutes remaining.
But three goals in eight minutes from Cecilio Waterman, Cesar Yanis and Eric Davis sealed a remarkable comeback for Panama, who are now fourth with 11 points.
In the day's other game Jamaica and El Salvador played out a 1-1 draw in Kingston.