Podolski fired the Gunners ahead in the first half after Cazorla played him through on goal. The Spaniard then doubled the visitors’ lead when he slotted the ball under Pepe Reina in the 68th minute.
An hour earlier, Fabio Borini had created the first chance of the game when he sped through the middle of the park but dragged his shot wide of Vito Mannone‘s post.
Moments later Luis Suarez injected pace to spin away from Per Mertesacker and leave the defender no option but to hack him down on the edge of the area.
Anfield held its breath in anticipation of a Manchester City re-run from Suarez but the Uruguayan blazed his free kick over the bar.
A move which started with Joe Allen breaking up the play and finding debutant Nuri Sahin ended with Borini cutting in from the right flank and arrowing into the Anfield Road end.
Cazorla had hearts in mouths when he wriggled free of Steven Gerrard and sent a low effort crashing towards Reina, but the Spaniard stood firm.
Former Everton midfielder Mikel Arteta stroked the ball about the middle of the pitch for Arsenal, while new recruit Cazorla found space to weave passes through tiny gaps in the Reds’ defense and the home side was forced to endure a spell without possession.
But the Reds fought for the ball. First Borini threw himself at the feet of Kieran Gibbs, then Gerrard clattered into Podolski and Allen charged in behind them to pick up the pieces and redistribute the play.
Anfield was on its feet when Raheem Sterling seized a loose Mertesacker pass and charged towards goal as Borini and Suarez darted off in opposite directions ahead of him.
But before the 17-year-old could pick a pass, he was bundled to the deck by Arteta and the Reds were awarded another free kick in a similar, dangerous position. However, Gerrard fired it straight into the wall.
Then Arsenal broke the deadlock with a lethal counter-attack.
Cazorla accelerated towards goal and Olivier Giroud spun away to his right, dragging Daniel Agger and Martin Skrtel in opposite directions.
Skrtel was subsequently forced to come and close the angle on Cazorla and the Spanish playmaker rolled the ball past him into the path of Podolski, who took one touch and arrowed past Reina.
The Reds threatened to hit back immediately. Gerrard shipped a pass out to Borini, who stretched and hooked the ball across the face of goal. Arsenal cleared only as far as the Liverpool captain, who nodded the ball to Sterling and signalled for the return pass.
However, the diminutive winger had other ideas. Dropping the shoulder, he twirled away from Carl Jenkinson and sliced the ball into the post with his left foot.
Minutes later Arsenal almost doubled its lead. Abou Diaby surged forward, covering almost 50 yards of the field, and Giroud’s movement had the Liverpool defense in disarray once more. However, when Diaby nudged the ball into the Frenchman’s feet, his composure deserted him and he sliced the ball into the Kop.
Five minutes after the interval, Gerrard found space down the right wing and hurtled towards the by-line before sliding the ball across the edge of the six-yard box, where Suarez was arriving but the Uruguayan was bundled to the floor by Mertesacker. Despite the Kop’s desperate appeals, no penalty was awarded.
Stewart Downing took to the field to replace Borini and on 57 minutes he found himself on the edge of the box surrounded by Arsenal defenders.
Composed, the winger back-heeled the ball to where Suarez was lurking and the Uruguayan fired at goal only for Mannone to palm his shot over.
The Reds were undone for a second time in the 68th minute. Cazorla exchanged passes with Giroud on the edge of the Liverpool box before ploughing into the Liverpool penalty area and hammering the ball under Reina for 2-0.
Liverpoolfc.com journalists’ man of the match: Joe Allen.