Cologne victory improves standing
Frank Schafer's side, who stunned champions Bayern Munich 3-2 last weekend, were quick off the mark and one up through Podolski after just three minutes and, although Sami Allagui levelled, Novakovic soon restored Cologne's lead.
Podolski and Novakovic were each on target again in the second half to seal another impressive victory - and lift Cologne out of the drop zone despite a late consolation from Mainz substitute Petar Sliskovic.
The match could hardly have got off to a better start for Cologne with Podolski's left-footed blast finding the bottom-left corner within three minutes.
Mainz were level just after the half-hour when Allagui collected Adam Matuschyk's headed clearance and smacked a left-footed shot into the centre of the goal. The visitors were not back on level terms for long, though.
Two minutes before half-time, Martin Landig headed Christian Clemens' free-kick back across goal and, although goalkeeper Heinz Muller got his hands to the ball, he could not hold on and Novakovic nodded in.
Mainz went within a whisker of drawing level for a second time seven minutes after the break, but Nikolce Noveski saw his close-range shot hit the post following a Christian Fuchs free-kick. Cologne then put the game out of reach with two goals in six minutes.
First Podolski latched onto Slawomir Peszko's pass and outsmarted Muller with a neat left-footed shot in the 55th minute, and then Novakovic got the better of two Mainz defenders before slotting home a fourth. Mainz pulled one back in the closing moments when Sliskovic fired home from Fuchs' pass, but it was not enough.