Olympiakos go top in Greece
Ernesto Valverde's team, PAOK, AEK Athens and Atromitos have all collected nine points but the Reds have played the least games and the victory preserved their 100 percent start to the campaign.
All the goals came in the first half of what proved a pulsating encounter at the Georgios Karaiskakis stadium.
PAOK were gifted the opener when home goalkeeper Franco Costanzo flapped at a corner and Sotiris Balafas turned the ball into the net from close range in the 25th minute.
The Reds restored parity 10 minutes later when David Fuster, who also scored in the 2-1 defeat at Arsenal in the Champions League last week, met a Vassilis Torosidis cross with a header.
The hosts took the lead three minutes before half-time when striker Raffik Djebbour headed home a Kevin Mirallas cross from the right.
AEK put their midweek Europa League disappointment behind them with a 1-0 win at Panionios, defender Kostas Manolas scoring the only goal with a header late in stoppage-time.
AEK also have nine points from four games and Panionios have collected seven from five.
Panathinaikos were without a fixture due to the ongoing legal disputes over which teams are to replace those relegated in the aftermath of the match-fixing scandal.
While Olympiakos Volos and Kavala were both relegated to Greece's second tier in July for their involvement in match-fixing, Asteras Tripolis were demoted to the second division after being found guilty of bribery.
Three places in the 16-team Super League are still to be filled with five rounds of matches played, causing a backlog of postponed fixtures.
The Super League has confirmed that the Professional Sports Committee (EEA) is expected to announce the decision on the licences of Doxa Dramas and Levadiakos, who are due to take the places of Volos and Kavala, on Tuesday.