The Manchester City forward kept his incredible form going by scoring once in the first half and twice after the restart, taking him to 24 goals for the season for club and country.
Harry Kane also converted from the penalty spot and Tomas Kalas rounded off the scoring six minutes from time with a comical own goal as England netted five times at Wembley for the first time since 2014.
Bulgaria's 1-1 draw with Montenegro in the other Group A fixture to take place today means that England top the early standings ahead of their trip to Podgorica on Monday.
Gareth Southgate was forced into an early reshuffle when Eric Dier suffered another injury setback as he limped off the field following a strong challenge from Tomas Soucek, leading to the introduction of Ross Barkley.
That change further disrupted the hosts' flow and it took until the 23rd minute for the first shot to arrive, coming via Czech captain Vladimir Darida, whose attempt sailed high and wide.
England were in front a minute or so later, though, as a flowing move of 25 passes, which included a touch or more from 10 of their 11 players, culminated in Jadon Sancho getting in behind Filip Novak and latching on to Kane's first-time reverse pass.
Sancho played the ball across goal for Sterling to slide in at the back post, making it three goals in three England appearances for the in-form forward.
The visitors enjoyed the odd spell on the ball, but they never once looked like troubling Jordan Pickford in the first half - Darida's poor attempt included - and they soon found themselves two behind.
Sterling got on the end of Dele Alli's backheeled pass and was sandwiched by Pavel Kaderabek and Kalas, giving Kane the chance to notch his sixth successful international penalty in a row, though Jiri Pavlenka got something to the ball and should have kept it out.
Jaroslav Silhavy's men managed three times as many attempts in the first 10 minutes of the second half as they did in the entire first half, with David Pavelka shooting straight at Pickford, substitute Matej Vydra seeing a flick-on kept out and Soucek glancing inches wide.
After waking from their slumber, though, England made sure of the points through another Sterling goal.
Moments after full debutant Sancho was denied by a block in front of goal, Sterling profited from some good central play from Kyle Walker to curl the ball inside the post.
Sterling completed his hat-trick six minutes later by collecting the ball from Barkley, cutting inside and sending it past Pavlenka, though only thanks to a big deflection off Ondrej Celustka.
Chances came and went for Patrick Schick and Vydra, as well as for Kane at the other end as he met his match in Pavlenka, but there was still time for England to score a fifth.
Hudson-Odoi raced inside from the left flank and got a shot on target that Pavlenka did well to push aside, only for the loose ball to hit Kalas and trickle into an empty net, the defender unable to adjust his body in time to make the clearance.
ENGLAND (4-3-3): Pickford; Walker, Keane, Maguire, Chilwell; Henderson, Dier (Barkley 17'), Dele (Rice 63'); Sancho, Kane, Sterling (Hudson-Odoi 70')
CZECH REPUBLIC (4-2-3-1): Pavlenka; Kaderabek, Celustka, Kalas, Novak; Soucek, Pavelka; Gebre Selassie, Darida (Masopust 67'), Jankto (Vydra 45'); Schick (Skoda 82')