Zlatan Ibrahimovic, Edinson Cavani and Lucas Moura scored PSG's other goals, giving Laurent Blanc's unbeaten side a seven-point lead over promoted Angers at the top of the standings after just 11 weeks.
Kurzawa, who joined from Monaco this summer, has endured a tough start with PSG, where he remains behind Maxwell in Blanc's pecking order.
The France international, who has not been called up for France's latest matches, was given only his third start.
In the 23rd minute, Kurzawa was played in by Marco Verrati in the back of the Saint-Etienne defense and slotted home with a cool finish after getting past defender Francois Clerc on the left side of the area.
PSG camped in Saint-Etienne's half and created two more chances before the interval through Angel Di Maria and Cavani but keeper Stephane Ruffier was well positioned to block their shots.
After a disappointing goalless draw against injury-hit Real Madrid in the Champions League midweek, PSG's forwards were more convincing. Cavani gave PSG more room to breathe in the 48th minute at the end of a counterattack after connecting with a cross from Ibrahimovic, who found the net in the 67th minute from Cavani's assist at the conclusion of a move ignited by Di Maria.
Saint-Etienne reduced its deficit in the 73rd minute when Marquinhos failed to clear the ball and shot straight at Verrati, who beat his own keeper. The Italian made amends with three minutes left to play with a good cross that Lucas headed in.
Earlier, Bernardo Silva scored to give Monaco its first league victory in a month with a 1-0 win at Reims while struggling Marseille ended a seven-match winless run.
Monaco dominated throughout with attractive attacking football to extend its unbeaten run in all competitions to 10 matches.
On the verge of crisis, Marseille bounced back with a 2-1 win at Lille with goals from Michy Batshuayi and Romain Alessandrini. Reims defender Sebastien Corchia ensured a nervy finish by pulling one back in the 71st minute but Marseille goalie Steve Mandanda made two decisive saves in a stirring final 10 minutes.
Marseille's first win in six league games — its first away victory this season — lifted the nine-time champions four points above the relegation zone.
With eight goals, Batshuayi is now the league's top scorer ahead of Nice's Hatem Ben Arfa. The Belgium striker scored from the rebound after Alessandrini's attempt from Lucas Silva's superb lofted ball hit the right post in the 37th minute.
"This is a great win, we were in an emergency situation and we needed the points," said Alessandrini, who doubled Marseille's lead with a shot from the edge of the box into the top left corner. "We proved that we can be united, score goals and win. This is a great relief, and hopefully this is just the beginning."
At Reims, Silva scored his third goal of the season in the 11th minute with a header from close range off Guido Carrillo's cross as Monaco moved to eighth place, 12 points behind PSG.
Reims slumped to a third straight loss that left the Champagne side lagging two points behind Monaco in 11th.
"I'm only interested in winning points for my team," said goalkeeper Johny Placide, who made a series of saves but was powerless to block Silva's header. "These three consecutive losses are annoying. We are lacking aggressiveness."
Monaco could have added a couple of goals before the interval but Carillo hit the woodwork twice in the first half and Placide thwarted a fine volley from former France midfielder Jeremy Toulalan.
Reims was reduced to 10 men in the 68th after Antoine Devaux was sent off for a second yellow card. The hosts played better after Devaux's dismissal and their best chance came in added time. Jordan Siebatcheu fired a low shot onto Danijel Subasic's post after taking advantage of a bad clearance from the Monaco defense.
Also, teenager Adam Ounas scored the lone goal as Bordeaux moved six points clear of the relegation zone with a 1-0 win over last-place Troyes.
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