Arsenal were indebted to goalkeeper Petr Cech - at fault for West Ham United's goals in a 2-0 opening-weekend defeat - in the first half after he produced a string of stunning saves to keep an impressive Liverpool at bay.
Arsenal improved and enjoyed the better of proceedings in the second half but were unable to breech a stingy Liverpool defence which has yet to concede in three matches this season.
Liverpool sit third with seven points - two behind early pace-setters Manchester City - while Arsenal, touted as serious title contenders before the season, have had an indifferent start and are ninth with four points.
“When you start your first game with a new club and everything goes wrong for you individually you need to go back to work and bounce back and this is what I tried to do,” Cech told Sky Sports.
“I was in the right place at the right time and I helped the team overcome difficult moments in the first half. It's hard to believe after all the chances it finished 0-0.”
Having been humbled 4-1 on their last visit to the Emirates Stadium, Liverpool made an early statement on a wet night in north London with Philippe Coutinho rattling the crossbar in the third minute.
That early scare brought Arsenal to life and only the narrowest of offside decisions denied Aaron Ramsey an opening goal five minutes later.
Arsenal were without experienced defenders Per Mertesacker and Laurent Koscielny and their replacements Gabriel Paulista and Calum Chambers looked nervous against the physical Christian Benteke and skilful Coutinho.
Arsenal commanded the majority of possession but it was Liverpool who carried the greatest threat against the hosts' disjointed defence.
Cech was called into action to deny first Benteke, with a stunning reaction save, and Roberto Firmino in quick succession.
Cech had to be at his brilliant best again to tip Coutinho's goal-bound shot onto the woodwork as Arsenal desperately held on before halftime.
The Gunners came out with far more conviction after the break and Santi Cazorla and Olivier Giroud combined to create a the space for Alexis Sanchez to fire against the post.
Liverpool were proving a tough nut to crack with Giroud, Ramsey and substitute Alex Oxlade-Chamberlain were all denied by Simon Mignolet as the visitor's defence stood firm.
Original source: Arsenal, Liverpool battle to a draw