Bournemouth snatched a last-gasp equaliser away at Watford on the weekend while at the same time City were thankful for a late Nahki Wells penalty, helping them avoid consecutive home defeats as they drew with Swansea City.
Alongside league-leaders Reading, Bournemouth are the only other unbeaten side in the Championship and showed their fighting spirit against Watford to come away with a point.
Mepham went from zero to hero after his error allowed Cardiff City in to score and earn a 1-1 draw in South Wales. Three days later, the Wales international was in the right place at the right time to grab just his second goal for Cherries, deep into stoppage time for another 1-1, this time at Vicarage Road.
Against City, they will again face up to stern opposition and a team who - much like themselves - have their eyes set on mounting a real promotion challenge.
What will concern Cherries boss Jason Tindall is that since taking ten points from their opening four games, they have since drawn three on the spin, all of which have been low-scoring encounters.
Still, the Cherries sit in fourth place and will be aware that if they can string a few wins together, they could find themselves in the top two, such is the nature of the Championship.
Unlike Bournemouth, Bristol City have not quite shown the same consistency in recent weeks, and Dean Holden's side will be looking to put recent results behind them right away.
After winning their first four, the Robins have slipped to two draws and a home defeat to leave them five points adrift of leaders Reading.
City's slip in form has largely been down to their dip in attacking threat. Holden has begun rotating his front men and may continue to see mixed results until he finds himself with a settled starting lineup.
After facing Bournemouth, City will ready themselves for a tough fixture at home to Norwich City but will be buoyed by the fact that they have not lost to the Canaries in their last seven meetings.
Bournemouth Championship form: DWWDDD
Bournemouth form (all competitions): LWWDDD
Bristol City Championship form: WWWDLD
Bristol City form (all competitions): LWWDLD
Chris Brunt - who made his first start in two years - may well get consecutive starts given Holden's injury woes.
As for Jason Tindall's selection, he believes this season's packed schedule played a part in the injury suffered by Jefferson Lerma against Watford and will have to assess the severity of the hamstring injury ahead of Tuesday's night's fixture.
Bournemouth possible starting lineup:
Begovic; Mepham, Cook, Rico; Stacey, Billing, Gosling, Smith; Stanislas, Solanke, King
Bristol City possible starting lineup:
Bentley; Vyner, Moore, Kalas; Hunt, Paterson, Bakinson, Brunt, Rowe; Wells, Martin
We say: Bournemouth 1-1 Bristol City
Both sides will be looking to get back to winning ways, but equally, neither will want to lose this one and that is why we are expecting the early exchanges to be cagey. As the game opens up, we can see Bournemouth being the stronger of the two sides and they may well take the spoils.