Even when the visitors were reduced to ten men after substitute Jon Beswetherick was sent off for two late challenges on Jimmy Turner in the space of 17 minutes, the Lambs could not force a breakthrough.
Both sides were tipped as relegation fodder before the start of the season but had been buoyed but tremendous victories on the opening day of the season.
Honours remained even in the first half although Tamworth's on-loan keeper James Dormand had to pull off two good saves to deny Scott Rendell and Sekani Simpson.
Meanwhile, Tamworth's more direct approach created problems for Rovers as Simon Hollis volleyed narrowly wide and Hugh McAuley was inches away with a fierce drive from 20 yards out.
The Lambs dominated the second half and Rovers had Ryan Clarke to thank for two tremendous saves. He bravely dived at the feet to deny Julian Alsop, who rejected Rovers in favour of the Lambs during the summer, and substitute Bob Taylor.
Ironically, once Rovers were reduced to ten men they plugged the defensive gaps and held out for a deserved point.
"It was frustrating because after beating Aldershot on the opening day, our supporters thought we would beat Forest Green easily," said Lambs boss Mark Cooper.
"But they are now full-time and are very hard working. They will surprise a lot of teams this season, just like us."