Gareth Southgate's side had already claimed top spot in Group A but put in a commanding performance over the second-place outfit ahead of next years European Championships
The West Brom youngster latched onto Nathan Redmond's cutback to give Gareth Southgate's side a first-half lead before finishing off Harry Kane's through-ball to double his tally shortly after the break.
Kane put the result beyond doubt six minutes from time after combining with fellow Tottenham man Tom Carroll and finishing low across goal.
It was a deserved victory for England as they rounded off their European Championships qualification with another victory and finished Group A with a record of eight wins and two draws in 10 games.
Berahino tested Alexei Koselev with just 10 minutes on the clock after Redmond found him from the right-hand side.
The pair linked up just three minutes later, however, with Berahino finding the back of the net with a strong header.
Redmond was lively throughout and could, and perhaps should, have doubled the visitors' lead 15 minutes later but was twice thwarted by smart saves.
But it was Berahino again minutes after the break to put a lacklustre Moldova side to the sword, skipping onto Kane's pass to round the keeper and slot home.
The 21-year-old, though, wasted a number of chances to seal his hat-trick with Koselev making amends for being caught out of position for the Baggies' man's second.
Manchester United’s Tyler Blackett then replaced Luke Garbutt in the 81st minute to make his Under-21s debut before Kane recovered from a poor first touch to add a third minutes later.
England will be among the seeded teams in Friday’s play-off draw where they will face the runners-up from one of the other nine groups.