The first set was an evenly-matched affair, with both players giving little away off their own service games.
The set went to a tie-break, which Berdych claimed 15-13.
The Czech player then made an early breakthrough in the second set, breaking the Raonic serve on his way to establishing a two-game advantage.
Raonic had the opportunity to level the scores in the seventh game but he failed to capitalise on a break point, which allowed Berdych to maintain his lead.
The world number seven held his nerve to serve out the set 6-4 and book a place in the quarter-finals.