Ross Lafayette was given his competitive debut over Jon Main and almost gave Welling the lead after one minute but was denied by a excellent save by Bath City's goalkeeper Glyn Garner.
After controlling the game for 20 minutes Welling fell behind as Aaron Brown's speculative long range shot saw Sam Mott parry the ball into his own net trying to lift the ball over the bar.
On 57 minutes, the Wings equalised after Baker's cross from the left was headed across goal by Luis Cumbers and found Lafayette who bundled the ball into the net for this debut goal.
Welling almost grabbed a 90th minute winner when substitute Scott Kinch was denied by another excellent Garner save who tipped the ball onto the post.
Jamie Day will be hoping for a response from his players when they travel to Chelmsford City - who like Welling are tipped for the playoffs - on Monday.