Tahirovic scored the only goal of the game - a wickedly hit strike from the edge of the box - midway through the first half to ultimately decide the game, as goalkeeper Davide Mastrantonio also saved a dubiously-awarded penalty in Sardinia.
The hosts had other chances but were thwarted on further occasions by Mastrantonio, as Alberto De Rossi's side moved 11 points clear at the top of the standings.
"Cagliari are a really good side, the league table shows that and today's performance only underlines it," De Rossi said.
"They amaze me a bit, they have this squad of small, quick, tricky players that can cause a lot of problems. My boys knew they had to dig in though and did that well.
"We could have scored a second goal, but equally you can't say it would have been unfair if Cagliari had managed to get a draw out of it. Individual quality [from Tahirovic and Mastrantonio] decided the game today but I have to reiterate that the whole squad dug in to secure this win."
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