Arsene Wenger was remaining patient during the week and he would have been thrilled with that call as two of the players he signed to replace Robin van Persie stepped up and got the goals required, making it two from two at Anfield after the Dutchman's brilliant double in the 2-1 triumph last season.
The day kicked into gear just after the half-hour mark when Podolski received a clever ball from Cazorla with the German taking a neat first touch before slotting home with his trusty left foot.
Cazorla fired just wide with a lashed effort from range moments before he also scored his first Gunners goal when he played a one-two with Podolski prior to hammering a low attempt goalward which found its way in under Pepe Reina.
Late on, Brendan Rodgers' Liverpool came at the visitors with substitute Jonjo Shelvey testing Vito Mannone with a dangerous effort but Thomas Vermaelen was on hand to produce a timely clearance as Steven Gerrard and Luis Suarez pounced.
Moments later, Suarez was played in by Gerrard but the Uruguayan's effort was seen over by a determined Vermaelen who was right on his hammer before Mannone was able to again deny Shelvey from range as the Reds finished with a flurry.
The loss forced Liverpool's worst start to a league campaign in 50 years with just one point from three outings whilst Arsenal produced three clean sheets to start a campaign for the first time in 88 years to go seventh on the table.
Anfield, Liverpool - 44,932