Both players began the match strongly as neither gave away a break point on serve, forcing a tie-breaker to decide the first set. However, the number six seed's class was to prevail as he claimed the tie-breaker 7-2 to take the lead in the contest.
Berdych found his form in the second set, and although Melzer made inroads on his serve, he produced the quality to fend off his challenge and take the two break points he earned to take a 2-0 advantage on sets in the match.
The 29-year-old compounded his advantage by earning an early break in the third set and he was able to slowly edge towards victory, before his second break of the Austrian confirmed his win by taking the set 6-3.
The number six seed will face Guillermo Garcia-Lopez in the next round of the competition.