08 stumble and nearly stall (but doesn't)

Been a few weeks and no complaints or issue from the car. Thanks to all who replied.
 
My '08 (with 300,000km and still the orig battery) stumbled a coue of times tonight driveing on the highway. Sharp jerk, but it kept going. Happened twice. I know this morning it struggled to crank (-13C - first really cold morning) more than usual and I thought that I should replace the battery. How can an old worn out battery cause a stumble in the engine?
 
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