Not only did Bath claim a valuable four points, they also denied Quins of a bonus point thanks to Tindall's try with only five minutes to go, as he found himself on the end of a move started by a fine chip from Olly Barkley.
Barkley kicked three first half penalties and two conversions in all, his other conversion coming courtesy of Ireland centre Maggs' earlier try on 14 minutes.
Quins included returning England wing Dan Luger for the first time since his latest lengthy injury lay-off, the former Saracen lasting just over 30 minutes after a long spell on the sidelines with knee trouble.
The Londoners had only three penalties from Irish fly-half Paul Burke to show for their efforts, despite applying late pressure, as they aim to avoid being pulled in to the relegation struggle.
BathTries: Maggs, TindallCons: Barkley 2Pens: Barkley 3
HarlequinsPens: Burke 3