Only seconds after Wilson had crumpled to the deck in a heap, Wellington tighthead prop Jeffery Toomaga-Allen scored the home side's first try as they took an early 10-0 lead following an earlier penalty from Lima Sopoaga.
Tim Bateman then scored Wellington's second when he waltzed through a gap that was a mile wide - Moses didn't have it that easy when he crossed the Red Sea - and bolted 30 metres to the line.
A paltry crowd of 2448 were subjected to strong gusts of wind at the Cake Tin, which caused havoc at lineout time and proved tricky to navigate for the goalkickers.
Sopoaga's continued influence off the kicking tee proved useful as Wellington took a 20-6 lead to the break.
Bay of Plenty began the second half in enthusiastic fashion as a botched clearance from their own line bounced fortuitously and led to a break-out try from fullback Dave Thomas as they stormed back in to the game at 20-13 following Willie Ripia's simple conversion.
Penalties punctuated the middle stages of the second spell though and Wellington will look for more finesse on attack when Canterbury come to town next Saturday night.
Eventually, Wellington No 12 Shaun Treeby scored in the 68th minute to ensure the win was safe.
With Wellington's mounting injury toll they will be pleased to get past Bay of Plenty with another win but coach Chris Boyd will know they need to be better when the defending champions pay a visit in round six.
Wellington (Jeffery Toomaga-Allen, Tim Bateman, Sean Treeby tries; Lima Sopoaga 4 pen 3 con), Bay of Plenty (Dave Thomas try; Willie Ripia 3 pen con) Halftime: 20-6.