Danny Nardiello opened the scoring against his former club early on before David Wheeler equalised late on in the first half. Bury re-took the lead a minute into the second half through Nathan Cameron before Nichols struck late on to deny Ronnie Jepson's side.
The afternoon didn't start too well for Bury as Tommy Miller dropped out of the starting eleven in the warm up after complaining that he felt faint after suffering from a bug through the week, Andy Procter was his replacement in centre midfield.
Exeter started the better of the two teams are nearly opened the scoring in the 10th minute but Danny Hylton and Shaun Beeley were wary of the threat and both cleared almost on the line.
Danny Nardiello then opened the scoring in the 14th minute when he received the ball on the right hand side of the area from a Craig Jones flick on. Nardiello then turned Scott Coles and fired an effort through the hands of Artur Krysiak and into the bottom corner to give the Shakers the lead.
The Rotherham loanee was again involved in the action five minutes after his goal when he set up fellow Rotherham loanee Danny Hylton. He fired a low effort towards goal and it was met by the sliding Hylton but Krysiak made sure he didn't concede two in quick succession and made a wonderful save to keep it at 1-0.
The game could have been over in the 28th minute when a long ball by Dean Howell caused confusion in the Exeter back line and the momentary lapse allowed Hylton to get on the wrong side of Coles. Hylton drove towards the edge of the area and unleashed a strike towards the far corner but his effort flashed just wide of the post.
Exeter then punished the missed chances shortly before the half time whistle when David Wheeler struck a left footed volley past Brian Jensen. John O'Flynn flicked Craig Woodman's throw in into the area with his first touch and Wheeler beat. Howell to the ball to leave Jensen stranded and Exeter level.
Bury didn’t let the Exeter goal get their heads down and came out firing in the second half. They got their reward one minute into it when Chris Sedgwick whipped in a corner. Nathan Cameron rose highest and headed past the defender on the line to give the 123 traveling Bury fans another goal to celebrate.
Ten minutes after Bury’s second goal, they thought they had a third when Tom Soares headed towards goal following a goal mouth scramble. The linesman and referee agreed that the ball didn’t cross the line but all the Bury players and fans believed it gone over and the player had stopped it with his hand. Neither decision went in Bury’s favour.
Exeter got their equaliser in the 76th after heavy pressure on the Bury goal. Liam Sercombe played the ball across the area and he picked out Tom Nichols who fired in from close range to square the game.
The Shakers brought on Danny Mayor with 10 minutes to go but he couldn’t get a winner for Bury but they did go close with Danny Nardiello and Tom Soares having half chances. Nardiello headed onto the roof of the net from the penalty spot before Krysiak pulled off a great save to deny Soares.
The result means Bury have now gone five games unbeaten and leaves them 20th in the league ahead of a tough trip to Cambridge on Tuesday night.
Bury: Jensen, Beeley, Cameron, Edjenguele, Howell, Jones, Procter, Soares, Sedgwick (Mayor 79), Hylton, Nardiello