Wrexham recovered from their first defeat since September in midweek to claim their seventh straight home win.
Full-back Curtis Obeng scored an early opener with a composed finish after a quick exchange with Jake Speight.
Bottom club Bath were denied an equaliser when Joslain Mayebi saved well from Marley Watkins, who then saw another effort cleared off the line.
Striker Speight doubled the lead soon after the break with a penalty after being brought down by Mark Preece.
The top-scorer took his tally to 13 for the season, and his return to the side relieved Dean Keates of the penalty duties after his last-minute miss from 12 yards in Tuesday's defeat by Forest Green.
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Wrexham manager Andy Morrell told BBC Radio Wales:
"It was a bit too open for my liking, they had a few too many shots, even though Josi (goalkeeper Joslain Mayebi) was comfortable.
"But I'm pleased. We talked about getting through the week this week - it would have been nice come through it with seven points by getting a draw on Tuesday.
"It wasn't to be but we're back to winning ways."
Wrexham 25 Mayebi 02 Obeng 03 Ashton 04 Creighton 06 Harris 07 Cieslewicz (Hunt - 63' ) 12 Keates (Colbeck - 81' ) 18 Tolley 20 Knight-Percival Booked 10 Speight (Anorllo - 90' ) 11 Morrell Substitutes 21 Maxwell 16 Hunt 26 Clarke 27 Colbeck 19 Anorllo Bath City 01 Garner 02 Simpson 15 Preece 26 Gallinagh 03 Stonehouse 07 Murray (Watkins - 16' ) 08 Connolly Booked 16 Canham 19 Burnell (Rollo - 90' ) 21 Russell 10 Phillips (Cook - 77' ) Substitutes 17 Matthews 04 Rollo 18 Watkins 09 Cook
Ref: Steve Martin