"I didn't make any predictions before the start of the season. I'm still curious to see how my team will play in the future. History still has to be written. It was a very heated atmosphere tonight. Marseille is a very good team but we knew how to wait for the right moment to score and to win."
Both teams also hit the woodwork in the second half, through Andrew Ayew and Kurzawa.
"We had a good first half but we lost a bit of concentration after the break, conceding such a quick goal," Marseille coach Elie Baup said. "There are encouraging signs for the rest of the season.
"It was a good match, very open. Both teams wanted to play football, to score goals. It was a nice spectacle, but for managers the spectacle is nice when you win."
Monaco moved top of the table with 10 points, one above Marseille and Saint Etienne, which earlier eased to a 2-1 home victory over Bordeaux, continuing its impressive start to the French league season.
Midfielder Romain Hamouma was the star of the match, scoring one goal and setting up the other. Hamouma put Saint Etienne in front in the eighth minute, volleying home Banel Nicolita's cross.
Fabien Lemoine almost doubled Saint Etienne's lead on the stroke of halftime, but his effort crashed off the right-hand post.
Saint Etienne did score a second on the hour mark with a diving header from Loic Perrin after Benjamin Corgnet had headed on Hamouma's free kick.
Bordeaux got one back in the final minute with a stunning strike into the top left corner from Ludovic Obraniak.
Allan Saint-Maximin made his league debut as the 16-year-old came on as a substitute for Saint Etienne in the 68th minute.
Saint Etienne has won three of its opening four matches and is unbeaten at home in 2013.
It is provisionally top of the table but will be replaced later when Marseille hosts big-spending Monaco looking to maintain its perfect start to the French season.
Nice and Montpellier both have five points after a 2-2 draw at the Stade du Ray.
Timothee Kolodziejczak headed in a corner for Nice in the 17th minute for the 21-year-old French defender's first league goal but Souleymane Camara leveled after dispossessing Nice's Jordan Amavi.
Nice restored its advantage three minutes from halftime when Valentin Eysseric controlled a long ball from Nampalys Mendy, feinted past Abdelhamid El Kaoutari and slotted home.
However, Siaka Tiene's 20-meter free kick, which flew just above the defensive wall, drew Montpellier level again seven minutes after the break.
Montpellier was reduced to 10 men for the final seven minutes after Djamel Bakar was shown a straight red card for a tackle from behind on Fabrice Abriel.