Berdych was forced into tie-breaks in both of the first two sets before winning the third with comparative ease to secure a straight-sets victory.
The number five seed looked ready to cruise to an early lead when he broke Kudla twice in succession to take a 5-1 lead in the first set.
However, the American fought back, surviving three set points and breaking Berdych twice to force a tie-break, which the Czech won 7-3.
Berdych once again took a commanding position in the second set when he broke in the third game, but he couldn't serve it out as Kudla broke back to force yet another tie-break, which again ended 7-3 to Berdych.
Kudla made a fine start to the second set when he broke Berdych in the very first game, but the Czech then wrapped up the set and the match in under 40 minutes, breaking twice to take it 6-3.