Inter Milan s Dutch defender Denzel Dumfries (R) eyes the ball during the Italian Serie A football match between Lazio and Inter on October 16, 2021 at the Olympic stadium in Rome. (Photo: AFP)
Anderson tapped home a rebound in the 81st minute to put the hosts 2-1 ahead at the Stadio Olimpico, with the Inter players furious that Lazio had not stopped play due to Federico Dimarco being down injured.
But Lazio were under no obligation to stop and Dimarco had hit the floor before Inter continued attacking themselves.
Five yellow cards were dished out in the aftermath as the away side's protests stopped play for several minutes, with visiting full-back Denzel Dumfries perhaps lucky to only be booked.
It was a miserable return to the capital for away coach Simone Inzaghi, who left Lazio in the close-season to replace Antonio Conte at Inter.
His Lazio replacement, Maurizio Sarri, has often been criticised in the early weeks of the campaign, but the three points take his new team into fifth place.
Inter remain third and could slip seven points behind pace-setters Napoli when they put their 100-percent record on the line against Torino on Sunday.
In Rome, Inter made the breakthrough in the 20th minute as Albanian full-back Elseid Hysaj clipped Nicolo Barella and Ivan Perisic stepped up to score for the second time this season.
Lazio responded well and almost turned their dominance of possession into an equaliser, but Toma Basic was denied by Inter goalkeeper Samir Handanovic.
The visitors retained a serious threat going forward, though, with Italy midfielder Barella curling over and Perisic forcing Pepe Reina into a fine save from his fierce left-footed strike before half-time.
But Lazio deservedly drew level in the 64th minute, after Alessandro Bastoni handled inside the area.
Immobile made no mistake with the penalty to net his seventh league goal this term and move above Inter striker Edin Dzeko at the top of the scoring charts.
The controversial moment came with nine minutes remaining as Dimarco went down holding his chest after appearing to be fouled in the centre circle.
But the referee waved play on and Inter's attack ended with Lautaro Martinez shooting straight at Reina, who started a quick counter-attack.
Immobile's shot was saved by Handanovic, with Anderson tapping in the follow-up. Dumfries and Handanovic responded angrily, with the Dutch wing-back almost ripping the apologetic Anderson's shirt.
Matteo Darmian became the sixth Inter player to be yellow-carded in injury time, and Sergej Milinkovic-Savic nodded in the resulting free-kick from Luis Alberto's delivery to seal the win.
Inzaghi's well-beaten champions continued to rage after the final whistle as Lazio celebrated.
Earlier, Spezia moved out of the bottom three with a 2-1 success against fellow strugglers Salernitana.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)