The Sweden international had never scored more than one goal in a single domestic season before, but he was superb as Cagliari ran riot - assisted by Inter captain Yuto Nagatomo's 27th-minute red card.
Cagliari went into the match bottom of the table with just one point and, although Pablo Daniel Osvaldo cancelled out Marco Sau's opener, Ekdal swiftly restored their lead just after Nagatomo's dismissal.
Samir Handanovic kept out Sau's 43rd-minute penalty with his 19th Serie A spot-kick save, but Ekdal netted either side of that, ensuring he doubled his total Cagliari goal tally inside 45 minutes.
Nemanja Vidic continuing his shaky start to life at Inter will have concerned Walter Mazzarri, with the hosts also displaying a lack of creative ingenuity in a second half which saw them fail to mount any kind of comeback.
Cagliari comfortably saw the match out to earn a first victory at Inter since 1995, while coach Zdenek Zeman claimed his first three points since taking over in July.
The calamities for the hosts began with just 10 minutes on the clock as Vidic and Nagatomo failed to cope with a long pass from the back and the ball made its way through to Sau, who lashed a half-volley home from the edge of the area.
Cagliari completely switched off in the 18th minute, though, as Inter drew level. Rodrigo Palacio played a quick free-kick into the left side of the area and the unmarked Osvaldo tapped in for an easy finish.
Inter's chances took a blow midway through the half though as Nagatomo received two second yellow cards in quick succession, the latter for a clumsy tackle on Andrea Cossu, and Cagliari capitalised almost instantly.
Handanovic was unable to keep hold of Daniele Dessena's fierce attempt and Ekdal knocked in the rebound.
Ekdal was decisive again a few minutes later, as Victor Ibarbo rampaged down the right and cut a pinpoint pass into the danger area, which the Swede coolly fired into the roof of the net.
Handanovic seemingly gave Inter a lifeline as he denied Sau from the penalty spot after the attacker went down theatrically under Vidic's challenge, but he was helpless from the resulting corner.
Inter failed to make the clearance and Ekdal smashed past Handanovic from point-blank range to give Cagliari a resounding lead in the 44th minute.
The hosts predictably piled the pressure on from the start of the second half and saw Osvaldo's 52nd-minute tap-in disallowed for offside.
That setback seemed to wipe out all Inter's confidence as they failed to test young goalkeeper Alessio Cragno sufficiently, Cagliari in fact going closest to the game's sixth goal as substitute Diego Farias hit the side-netting.
A lack of late action saw the visitors cruise to a victory which lifts them off the bottom but Inter's first defeat of the season leaves them already seven points behind Serie A pacesetters Juventus and Roma.
