Germany's Kohlschreiber began the contest brightly and claimed an early break of Andujar-Alba's serve to open up a two-game advantage.
A second break followed soon after, which allowed the world number 19 to claim the opening set in just over 30 minutes.
However, Andujar-Alba's response was positive in the second set and he inflicted the same damage on Kohlschreiber that he had received during the first set to force a decider.
A break early in the third set provided Andujar-Alba with two chances to win the match, but on both occasions Kohlschreiber battled back to level up proceedings and as a result a tie-breaker was required to determine a victor.
Having been made to hang on during large parts of the final set, Kohlschreiber claimed the initiative early in the breaker and eventually ran out a 7-3 victor.