Midfielder Leonardo Colucci put Cagliari ahead in the 17th minute and although the Italian champions equalised through Fabio Grosso, they failed to capitalise on their second-half dominance.
The draw left Inter third in the standings after AS Roma beat Empoli 1-0, thanks to a goal by striker Vincenzo Montella, and Palermo also won by same score at Chievo Verona.
Roma lead Palermo on goal difference with 12 points from five matches, with Inter a point adrift.
Inter's city rivals AC Milan also endured a frustrating afternoon, Siena keeper Alex Manninger pulling off a series of saves as the Serie A giants stuttered to their third 0-0 result in a row and slipped nine points off the lead.
Stung by their 2-0 defeat by Bayern Munich in the Champions League midweek, Inter's players were hopeful of a morale-boosting win over lowly Cagliari, even though they were missing midfielders Esteban Cambiasso and Patrick Vieira to injury and suspension.
A defensive black-out after 17 minutes, however, allowed Colucci to rush in unmarked at the far post and volley Mauro Esposito's cross past Inter keeper Julio Cesar.
Inter's problems got worse when striker Hernan Crespo hobbled off the pitch with a left leg injury.
The visitors worked their way back into contention and equalised seven minutes from the break, when Adriano nodded on a cross for Grosso to fire in a low volley.
In the second half Adriano, Marco Materazzi and Zlatan Ibrahimovic all went close to heading Inter into the lead but Inter were forced to accept a draw.
"It's a disappointing
"Even after Crespo was injured we continued playing well and created lots of chances."
Roma gave a more business-like performance at the Olympic Stadium.
Montella's second goal in two games confirmed his return to form after a long series of back and shoulder problems.
The 32-year-old striker almost made it 2-0 midway through the second half, when Daniele De Rossi put him through on goal, but he failed to chip Empoli keeper Daniele Balli.
Eugenio Corini's 30th minute strike was all Palermo needed to secure victory over Chievo.
The Sicilian side's playmaker pounced on a short clearance by defender Davide Mandelli to drill a shot into the net.
Milan's continuing failure to score after draws with Livorno and Lille in the past eight days will do nothing to quell the internal division within the squad that emerged this week when midfielders Clarence Seedorf and Kaka publicly criticised the tactics of coach Carlo Ancelotti.
"Maybe we lacked a bit of speed, but overall I thought we played well. Let's just say we're going through a bit of an unlucky patch at the moment," said Ancelotti.
Alberto Gilardino headed against the bar, Siena keeper Manninger saved a 30-metre drive by Andrea Pirlo, and Kaka put the ball in the net only for referee Nicola Stefanini to rule it offside.
Manninger capped a miserable afternoon for Milan in the final minute of stoppage time, when he pulled off a reflex save to push a Massimo Ambrosini header over the bar.