Riyad Mahrez scored the second-half winner at the Vitality Stadium to move Guardiola's champions two points above title rivals Liverpool ahead of Sunday's Merseyside derby.
City, who prevented the hosts from registering a shot on target, dominated proceedings and would have won by a far bigger margin had it not been for an inspired second-half performance from Cherries goalkeeper Artur Boruc.
Victory, however, came at a cost as the visitors lost the key duo of De Bruyne and Stones to injuries.
After City controlled the opening period without really threatening to score the Belgian, who has already had two lengthy lay-offs this term due to knee issues, limped off to be replaced by match-winner Mahrez in first-half stoppage time.
Centre-back Stones, returning following three games out, then had to come off for captain Vincent Kompany three minutes after the restart.
Guardiola believes the injuries are "physiological" issues, with the club's packed fixture list contributing to the problems.
"John, I think, is more a precaution, we'll see tomorrow. He was a little bit tight, he didn't feel good, and we didn't take risks. Hopefully it has not a big issue," he said.
"And Kevin has something with his hamstring. I don't know (how long he will be out), tomorrow we'll know exactly.
"But it's normal, my friends. We played 25 games in, I think, 93 days. It means every three days and a little bit more we play one game, so it's a physiological issue.
"These guys we demand play in that way every three days when the body is not already recovered, and of course sometimes the muscles say, 'hello, it's enough'."
Guardiola believed the performance on the south coast was one of the finest of the season.
"We make an incredible performance today, one of the best performance we ever played," he added. "We didn't concede one shot on target.
"Every time we lose the ball, we had three or four guys going there to pick up and recover the ball and play.
"They (Bournemouth) were incredibly well organised, 11 players in the box, there were really no spaces, and we found them.
"I don't know what's going to happen at the end of the season but these players deserve all my admiration, all my respect.
"It's incredible how good they played today. Today is a special moment for all of us."
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