Juventus, who are unbeaten in Serie A since the end of September, top the standings with 29 points, one ahead of Inter Milan who host mid-table Frosinone on Sunday.
“Fortunately (the goal we conceded) was irrelevant,” Juventus coach Massimiliano Allegri told DAZN.
“We need to be more effective in the last pass. The lads have an extraordinary spirit and they know that to bring home a win they have to play like this. Now we are more compact than at the beginning of the season.”
Bremer broke the deadlock on the hour mark with a towering header from a Kostic cross and Rugani doubled the lead 10 minutes later, bundling the ball in with his chest after hitting the bar following a corner.
Cagliari briefly silenced the Juventus Stadium when they pulled one back in the 75th minute through defender Alberto Dossena who nodded home from a corner.
After six consecutive clean sheets, Juventus conceded their first goal since the 4-2 loss at Sassuolo on Sept. 23.
Juve host Inter in a top-of-the-table clash on Nov. 26, following the international break.
“Inter are favourites for the Scudetto with AC Milan and Napoli a little behind,” Allegri added.
“They are a team that has been built for years to win the championship and this year they are the number one favourite. Today’s victory is useful for us to stretch the lead over those behind.”
Cagliari, who last weekend climbed out of the relegation zone with a 2-1 win over Genoa, are 17th on nine points.