In a match that was dominated by serve, Berdych got the better of his French opponent to take the match 6-3 7-6.
Berdych converted the solitary break point to take the first set 6-3.
Both players created several opportunities on the other player's serve during the second but both were unable to take advantage as the set went to a tie-break.
The tie-break went with serve until a double fault from Tsonga handed Berdych a 5-4 lead and the powerful Czech sealed victory with an ace to advance to the last four.
Berdych will now play either Novak Djokovic or Tommy Haas in the semi-finals.