Simone Zaza was both hero and villain for Torino as he gave it the lead shortly after halftime but was then shown a straight red card in the 73rd minute for dissent.
Cagliari immediately made the most of the numerical advantage as Leonardo Pavoletti headed in the equalizer. There were suspicions of offside but the goal was awarded after a lengthy video review.
Torino remained seventh, five points behind AC Milan and the final Champions League qualifying spot.
Montella, who previously coached Fiorentina from 2012-15, replaced Stefano Pioli on Wednesday.
Luis Muriel hit the post late on but Fiorentina extended its winless streak to nine matches.
Bologna inched three points above the relegation zone.
Elsewhere, Sampdoria beat 10-man Genoa 2-0 in a derby match. Gregoire Defrel gave Sampdoria an early lead before Fabio Quagliarella converted a penalty following Davide Biraschi’s handball, which also saw the Genoa defender sent off.
It was Quagliarella’s 22nd goal of the season, moving him one above Milan forward Krzysztof Piatek at the top of the scoring charts.
Also Sassuolo drew 0-0 against Parma, which had a penalty saved.
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