The Canadian improved to 2-0 against the fifth-ranked Berdych, beating the Czech star 6-2, 6-4 on Thursday night to advance to the Citi Open quarterfinals.
Berdych was the top seed in the hardcourt event.
Berdych unofficially committed 21 unforced errors and had his serve broken four times, including the final game of each set. Two of Pospisil's three career top-10 wins have come against Berdych, the first last year in Montreal.
Berdych trailed 0-3 in the first set and never recovered.
''The beginning was very key to the whole match,'' said Berdych, who described Pospisil as a player who does his best in big matches.
No argument from the 36th ranked player.
''I prefer center courts. I just prefer playing in front of people and on bigger stages. ...It's motivating,'' said Pospisil, who won the Wimbledon doubles title with American Jack Sock earlier this month.
Pospisil only lost serve once, fighting back three of four break points. He will next face No. 10 Santiago Giraldo, a 6-2, 6-0 winner over Victor Estrella Burgos.
Berdych said a tweaked back suffered at the start of the week limited his practice time.
No. 4 Kei Nishikori closed the evening session with a 6-2, 2-6, 6-3 victory over Lukas Lacko.
Johnson, ranked 68th, is turning into a giant killer. The fourth-highest ranked American on tour entering this week topped fifth-seeded John Isner in three sets Wednesday.
The 6-foot-2 Johnson fended off 27 aces by the 6-foot-11 Karlovic after the 6-foot-10 Isner had 29.
''Second day in a row (I had) to play somebody with a massive serve,'' said Johnson, who is 4-1 in tiebreakers this week. ''In a tiebreaker, anything can happen.''
Isner double faulted in the third set tiebreaker to set up Johnson with match point. The same scenario played out Thursday, though not until Johnson fended off two match points to even the tiebreaker at 6-6.
Karlovic's third double fault of the match gave Johnson, the two-time NCAA Division I singles championm an 8-7 lead.
After serving out wide to Karlovic's backhand, Johnson moved in to strike the soft return. He smacked a forehand winner into the corner to reach his fifth quarterfinal in his second full season on tour.
Next up, 6-foot-5 Raonic. The Wimbledon semifinalist ranks third in aces behind Isner and Karlovic.
''They're getting shorter every day,'' Johnson cracked.
Sixth-seeded Richard Gasquet beat Tim Smyczek 6-3, 6-2. Seventh-seeded Kevin Anderson also advanced, beating Malek Jaziri 6-3, 6-4. Donald Young beat No. 15 Denis Istomin 6-3, 3-6, 6-3 for his second straight victory over a seeded player.
In women's second-round play, second-seeded Ekaterina Makarova beat Lauren Davis 6-2, 6-4; fifth-seeded Anastasia Pavlyuchenkova topped Hiroko Kuwata 6-3, 6-3; sixth-seeded Svetlana Kuznetsova beat Kirsten Flipkens 6-4, 7-5; and Vania King routed Christina McHale 6-1, 6-3.