LONDON — Arsenal relied on Santi Cazorla’s stoppage-time penalty to secure a 2-1 victory over Southampton on Saturday after another unconvincing display from the London club as it chases a first Premier League title since 2004.

Faced with dropping points in its first home game since losing to Liverpool in the opening round, Arsenal benefited from a favorable refereeing decision 30 seconds after the clock hit 90 minutes. Jose Fonte dragged down Olivier Giroud with a tug on the striker’s shirt, referee Robert Madley pointed to the spot, and Cazorla converted.

“It’s a relief,” Arsenal manager Arsene Wenger said. “When you lose your first home game you cannot afford to drop points in the second home game because it creates a little bit an anxiety level at home and that’s not what you really want.”

Arsenal fell behind in clumsy circumstances in the 18th minute. Dusan Tadic’s free kick was pushed onto the crossbar by Petr Cech but the ball came back down off the Arsenal goalkeeper’s back and into the net.

Arsenal hadn’t managed a shot on target until that point. The hosts did score with their first effort in the 29th and it was a memorable way for Laurent Koscielny to mark his 31st birthday. In the goalmouth, the defender arched his body, connected with the ball with his right boot, and acrobatically kicked it over his head into the goal.

“We had a little bit of a slow start, after 20 minutes we were 1-0 down, so we came back well into the game and we had a good response,” Wenger said. “In the second half, I felt we dominated well again, created many dangerous situations, but couldn’t score.”

After picking up only one win from its first three games, it looked like being another frustrating day for Arsenal until Cazorla’s late intervention. The Gunners have now reeled off back-to-back wins but they remain five points behind leader Manchester City and looking far from being title challengers.

Southampton remains without a win four games into the season and new manager Claude Puel is frustrated that his team has conceded three penalties.

“This is too much,” Puel said, avoiding criticizing Saturday’s referee. “I want to stay with the positives of this game. We played the first 30 minutes fantastic. Good football, good possibilities.”

Southampton hosts Sparta Prague in the Europa League on Thursday. Arsenal’s European campaign begins on Tuesday with a Champions League game at Paris Saint-Germain.