“I said this week that winning is the best medicine,” Arteta said. “For sure this one is going to make us (feel) really good. I think it was a convincing win.”
He can also thank Lacazette.
It was his second straight goal after scoring a penalty in the 3-1 win against Chelsea on Saturday, where defeat may have cost Arteta his job.
Arsenal started sluggishly against Brighton but improved considerably after the break.
“It was a tricky game, very different from the Chelsea game,” Arteta said. “It took us a while for us to understand how we had to attack this block. But we talked about it, we came out (in the second half) and created four or five big chances straight away, and scored a really good goal.”
Lacazette was replaced as lone striker by Pierre-Emerick Aubameyang, who has been short of the form which made him arguably the league’s most dangerous striker last season.
Aubameyang has scored 57 Premier League goals since joining Arsenal nearly three years ago.
He should have had No. 58 when, with his first chance in the 50th minute, he met Saka’s left-wing cross but steered his close-range shot straight at goalkeeper Robert Sanchez.
Moments later, Arsenal’s 19-year-old Brazilian forward Gabriel Martinelli shot narrowly over the crossbar from just inside the penalty area, and then Aubameyang fluffed a counter-attack when he tried a difficult curling shot instead of picking out midfielder Emile Smith Rowe in a better position.
Saka went off late after taking a knock to his ankle, but the injury did not appear serious and he sat in the stands to watch the remainder of the encounter.
Brighton had the better of a drab first half, with Alireza Jahanbakhsh having a shot saved and shooting wide with another chance, with both attempts following crosses from Brazilian Bernardo.
On Saturday, Arsenal travel to next-to-last West Bromwich Albion, while 17th-placed Brighton hosts Wolves, who fell 1-0 to Manchester United on Tuesday after a 93rd-minute goal from Marcus Rashford.
West Brom, meanwhile, lost 5-0 at home to Leeds while Sheffield United’s campaign of woe continued with a 1-0 loss at Burnley. Southampton and West Ham played out a scoreless draw.