Ex-Cheltenham man Connolly netted Bath's first home goal of the season
Bath City came back from a goal down to beat Rushden & Diamonds and kick-start their Blue Square Bet Premier campaign.
The visitors took the lead after just five minutes when Max Porter latched onto Rene Howe's cross and tapped it in from six yards.
But 30 seconds into the second half, midfielder Adam Connolly curled a left-footed volley past keeper Dale Roberts to draw Bath level.
Adie Britton's side sealed the win thanks to a Darren Edwards header.
Bath City boss Adie Britton told BBC Radio Bristol: "I said to them [at half-time] we hadn't done ourselves justice, we were a little tense at times and didn't keep the ball well.
"To get a goal within in 40 to 50 seconds [of the second half] did an enormous amount for our confidence and made them a little apprehensive.
"It's a massive lift for the club as a whole as we've bought in a few players and you do wonder if you're good enough."
Rushden & Diamonds manager Justin Edinburgh told BBC Radio Northampton: "You never like to lose and the way we gave away the goals was disappointing.
"I thought we were good in the first half, defended well and could have got another goal.
"People expect us to be at the top - but if we concede goals like we did tonight we're certainly not going to be."
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