The 20-year-old US international defender played the full 90 minutes in Saturday's 4-0 victory at Aston Villa.
Miazga, 20, originally joined Chelsea from the New York Red Bulls in late January after enjoying a breakout season in MLS, but the American centre-back was limited to just one appearance for the Under-21s during his first two months in west London.
However, he finally made his first-team bow on Saturday with Gary Cahill and John Terry both out injured, starting the club’s trip to Aston Villa alongside Branislav Ivanovic in the heart of defence.
He certainly did not look out of place on the day either, putting in a flawless display as Guus Hiddink’s men cruised to a comfortable 4-0 win, and Klinsmann was delight to see the one-time capped defender make such a positive impact.
Speaking about the performances of his European-based Americans from the weekend, the German said: “I think the biggest highlight from a Premier League perspective for us was Matt Miazga playing his first game for Chelsea. This is a big one.
“It’s a big moment for us as a national team programme but especially for Mat to get his first introduction to the Premier League with Chelsea. I sent him a text straight after the game saying congratulations, so it’s really fun to see.”
Miazga’s emergence on the Premier League scene is all the more impressive considering he was not even a full-time starter in MLS until the 2015 season.
The New Jersey native, who holds a Polish passport by way of his parents, established himself as one of the league’s top talents over the course of the campaign as Jesse Marsch’s men won the Supporters’ Shield title, making 26 regular season appearances and scoring one goal.
His impressive performances prompted Klinsmann to hand the 6ft 3in stopper his senior US debut as a second-half substitute in November’s opening World Cup qualifier against Saint Vincent and the Grenadines, while he was also named US Soccer Young Male Player of the Year the following month.
Saturday’s start was another big step forward in his meteoric rise, and while he obviously remains a long-term project for Chelsea, it would not be a shock if he was pushing for regular minutes sooner rather than later given his rapid progress over the past 12 months.