The Three Lions were dealt an early blow at Wembley as Eric Dier was forced off on 17 minutes, with Ross Barkley replacing him, but they were unaffected by the reshuffle in midfield and capitalised on their early dominance by taking the lead just after the halfway point in the first half.
Jadon Sancho's cross from the right beat Jiri Pavlenka in the Czech Republic goal and Sterling slid the ball into an empty net to open the scoring.
England doubled their advantage in first half injury time as Sterling was brought down by Pavel Kaderabek inside the area.
Captain Harry Kane converted from the spot-kick, despite Pavlenka managing to get a hand to his effort.
The visitors gave England a few scares early in the second period as Slavia Prague midfielder Tomas Soucek headed narrowly wide from a free kick and David Pavelka produced a save from Jordan Pickford from a corner, but England's third just after the hour mark ended any chance of a Czech fightback.
Kyle Walker's pass ricocheted off two Czech Republic defenders into Sterling's path, and the Manchester City star hit a curling shot on the turn giving Pavlenka no chance in the away goal.
Sterling grabbed his third on 68 minutes with an effort from the edge of the area, with his effort taking a wicked deflection off Ondrej Celustka, for his first hat-trick for England.
Declan Rice and Callum Hudson-Odoi made their England debuts as second half substitutes and the latter played a key role in the fifth goal.
Hudson-Odoi's effort was saved by Pavlenka but Tomas Kalas somehow managed to turn the ball into his own net.
England head to Montenegro on Monday for their second match in Euro 2020 qualification Group A.