The Serbian displayed all the skill that has seen him reach the top of the men's game in the first set as he brushed aside his Spanish opponent 6-0.
Andujar Alba put up more resistance in the second as both players continued to hold serve and take the set to a tie break.
Andujar Alba controlled much of the tie break and eventually forced out his opponent 7-5.
The final set started badly for the Spaniard when he was broken instantly by Djokovic.
The world number one broke again in the seventh game before he served out the set 6-2 to book his place in the last eight.