Former England international James Milner gave Liverpool the lead on the 61 minute but this was cancelled out by a late strike from Lacazette.
The 27-year-old created separation from Reds keeper Alisson before curling in a sublime finish into the bottom corner in the 81st minute.
Arsenal have been in a good run of form of late, but have previously struggled to prove themselves against the Premier League’s top teams.
The Gunners suffered early season losses to Manchester City and Chelsea, but have since managed to put together a 13 game unbeaten run in all competitions.
Lacazette believes Arsenal’s performance against Liverpool is a demonstration of the quality they have within their ranks, to compete with the teams at the top of the table.
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“The first big game we lost but we knew if we work like we did for 12 games we can have points,” Lacazette said.
“We felt we had the quality to play the top of the league tonight.
“The first half was hard, but in the second half we were better and more physical.”
With the draw in north London, Liverpool have extended their unbeaten streak to 11 games and in the process have only conceded four goals.
Arsenal winger Alex Iwobi concedes a draw was a fair result and contributes the improvements seen within the squad to new boss Unai Emery.
“It was a difficult game with both attacking teams and I guess the fair result was the draw,” Iwobi said.
“We are giving extra intensity and you can see the manager demands a lot not just in games but on the training pitch and it is paying off.
“People say juice is banned but we do get it in the mornings so he is not too strict! It is not just the nutrition it is the attention to detail and tactics and you can see we are enjoying it.”