The fifth seed, who is chasing his first ever Grand Slam, had struggled somewhat in his tournament opener against Jiri Vesely but was in complete control against the Spaniard, cruising to an easy win.
He quickly grabbed the initiative, breaking his opponent early, while holding his own serve, to bag the first set.
The pair then traded two breaks each in a rollercoaster second set with Carballes Baena trying to lock Tsitsipas in long baseline rallies.
The Spaniard managed to take it to a tiebreak but the Greek kept his composure to take a two-set lead before cruising to a quick 4-0 and then booking his spot in the third round with ease.