Rodgers wanted a kick-start after a less than convincing start to the campaign. This win, and the manner of it, might just do that, although injuries will be of concern ahead of the visit to league leaders Hearts on Sunday.
Celtic needed to show more intensity and fight to start to get things back on track. They did, and overcame considerable adversity within this game to succeed.
They created far more chances than of late, but a lack of conviction in key moments might have cost them. To their credit, they stood up to the pressure, continued to create and, finally, got the reward they sought.
Having defeated Rangers earlier this month, Sturm arrived in good form and with confidence. At one stage, they easily could have had a two-goal cushion and you wonder what outcome might have followed if they had.
In normal circumstances you would fancy Celtic to take care of them at home. These aren't normal circumstances right now, but this might just be the shot in the arm they need to kick on.
With that top-of-the-table Premiership meeting to follow at Hearts, the potential lack of options up front will be a big challenge to overcome. Possible defensive ones, too.
Things, on a lot of fronts, haven't been going Celtic's way of late. Finally, they did at a vital time. On the balance of play, deservedly so, with yet more big challenges on the immediate horizon.