Goals from Christian Pulisic (two), Auston Trusty, Julian Hall, Weston McKennie and Folarin Balogun gave the US a commanding first-leg advantage, but they failed to settle the outcome of the quarter-final before Tuesday’s second leg in Cincinnati.
The build-up to Saturday's fixture in Miami had been overshadowed by news of Pochettino's departure as US coach after agreeing to take over Manchester United.
But there was little sign that news of Pochettino's exit had disturbed US preparations as they demolished World Cup qualifiers Haiti to deliver the biggest victory of the Argentine coach's two-year reign.
"Pochettino is an amazing manager and he's added a lot to us with the national team," goalscorer Balogun said afterwards. "It's always sad when you see a top coach leave, but it's a part of the sport.
"I think it was just important for us today to stick together and get the win - it just makes the send-off better," Balogun added.
Trusty gave the Americans the lead after just 10 minutes, confidently finishing from close range after Sebastian Berhalter's free-kick from the right flank.
That goal was all that separated the teams at half-time, but the floodgates opened after the break.
Hall calmly tucked away Antonee Robinson's low cross in the 52nd minute after a sweeping counter-attack to make it 2-0.
Pulisic made it 3-0 from the penalty spot 10 minutes later after being brought down in the box by Haiti defender Carlens Arcus.
Milan forward then grabbed his second goal a minute later, rifling into the bottom corner from the edge of the area to make it 4-0.
McKennie's 68th-minute header put Pochettino's side 5-0 up, and the US thought they had added a sixth soon afterwards when Balogun shrugged off Arcus to score from close range.
A VAR review, however, determined that Balogun had fouled Arcus in the build-up and the goal was chalked off.
Balogun did not have long to wait, though, for his 13th international goal, latching on to a Malik Tillman through ball to score in the 82nd minute.