The meeting lasted one hour and 30 minutes and ended with the score 6:4, 7:5.
The Russian tennis player converted four out of six break points, made five double faults and completed four aces.
The Spaniard made two errors on the pitch, did not complete a single serve right through and sold two breaks with five break points.
In the third round Alexandrova will face Marie Bouzkova from the Czech Republic.
Earlier it was reported that Russian Anastasia Pavlyuchenkova lost to Spaniard Sara Sorribes-Tormo in the first round of the WTA tennis tournament in Madrid.