Billy Paynter had put Rovers ahead but Matt Tubbs look to have secured the Cherries a point when he levelled just four minutes from time, only for James Husband to grab a winner moments later and condemn their hosts to a fifth-straight defeat.
Sheffield United remain in second place after they were held to a goalless draw by MK Dons, while third-placed Swindon drew 2-2 with Walsall.
Andy Williams gave Swindon the lead before Will Grigg equalised from the penalty spot for the visitors. Simon Ferry put Swindon back ahead but they were denied all three points by Jamie Paterson's late strike.
Steven Pressley enjoyed a winning start in charge of Coventry as the Sky Blues came from a goal down to beat relegation-threatened Scunthorpe 2-1 at Glanford Park. Akpo Sodje put the hosts ahead, but Carl Baker and Leon Clarke replied for Coventry.
Tranmere enhanced their promotion hopes with a 1-0 win over lowly Oldham thanks to Max Power's goal, while Yeovil were held to a goalless draw at Hartlepool.
Portsmouth moved off the foot of the table as they leapfrogged Bury - David Connolly grabbing both goals in a 2-0 win over the Shakers.
Carlisle were 2-0 winners over play-off hopefuls Brentford thanks to goals from Sean O'Hanlon and Mark Beck, while Crawley and Notts County played out a goalless draw.
Mathias Pogba got the winner for Crewe as they won 2-1 at Colchester. Alex had led through a Luke Murphy penalty only for George Porter to level, but Pogba made sure of the three points.
Leyton Orient won 2-0 at Shrewsbury thanks to strikes from Mathieu Baudry and a Kevin Lisbie penalty.
Goals from Lee Holmes and William Hayhurst also gave Preston a 2-0 win, against Stevenage.