City is back at the top of the table, with Liverpool needing to address a two-point deficit in the Merseyside derby at Everton after Mahrez snuck in his 11th goal of the season 10 minutes into the second half at the Vitality Stadium..
Yet the Algeria winger was only on the field because Kevin De Bruyne suffered the latest setback of an injury-ruined season.
Eddie Howe's side remains 12th after a far more robust showing than in its 5-1 loss at Arsenal in midweek, but it offered little attacking threat from its disciplined 5-4-1 setup.
David Silva shot wastefully wide from De Bruyne's 19th-minute cross, although the Belgium midfielder's half would end in dejection.
An audacious overhead kick from centre-back Nicolas Otamendi was the next closest City came to finding an opener before the interval – demonstrating how effectively Bournemouth restricted opponents who enjoyed 83 per cent possession in the opening 45 minutes.
The injury woes continued early in the second period for Guardiola, with John Stones lasting 47 minutes on his return before making way for Vincent Kompany and icing his thigh on the bench.
Mahrez eased frustrations of another kind in the away dugout when he drilled a shot under Artur Boruc after Silva worked possession into his path.
Raheem Sterling came close to scoring in a seventh consecutive match against Bournemouth but drove into the side netting in the 64th minute.
The England winger then turned provider as Boruc held a stabbed shot from Sergio Aguero, who later rattled the bar with a speculative strike.
Bournemouth's goalkeeper hared out to deny Sterling inside the final quarter of an hour before preventing the match-winner Mahrez from heading his second.