Martin Skrtel put the Reds ahead in the 33rd minute with a thundering header off captain Steven Gerrard's corner. City midfielder Yaya Toure equalised off right-back Martin Kelly's failed clearance.
Liverpool's influencial striker Luis Suarez put the Reds ahead immediately with a curling free-kick but Anfield's hero Skrtel turned Villan late in the second half as his disastrous back-pass was cut-off by striker Carlos Tevez who slotted home easilly past Pepe Reina.
Both teams had equal number of chances but Liverpool looked more threatening in the first half. 17-year old winger Raheem Sterling started his first League game for the Reds and did impress in the first 45.
Liverpool were lucky not to concede early on as Tevez's shot hit the post. Striker Fabio Borini saw his shot go wide after meeting Sterling's perfect cross. Brendan Rodgers men earned their first point of the new campaign after losing 3-0 against West Brom in their opening fixture.
Arsenal failed to seal three points yet again as they were held at the Brittania stadium by Stoke City. Arsene Wenger's Gunners finished 0-0 for the second-time running after being held by Sunderland in the opening fixture of the new season.
Although Arsenal dominated in terms of possession, they lacked any finishing touch in their opponents half. New signing Santi Cazorla pulled the strings in midfield while striker
Oliver Giroud failed to score yet again. The Gunners attempted 17 shots to Stoke's six as Tony Pulis' side were threatening on the counter. The Potteries winger Jermaine Pennant had a penalty shout denied after left-back Keiron Gibbs brought him down in the edge of the box.
Arsenal squandered many chances early on as Stoke were left open with a little share of possession.
Mikel Arteta had his free-kick blocked while midfielder Abou Diaby took too much time to get his short away inside the six-yard box. German winger Lukas Podolski also had his shots flying all over but not in the back of the net.
Another disappointing result for Arsene Wenger's side as they fail to kick-start the new season with a win minus Robin van Persie.