Losing three of their previous four matches has loosened Lazio’s grip on a top-four finish, and struggling Lecce looked hellbent on upsetting the Biancocelesti further.
The perfect opportunity to do just that fell their way when Elseid Hysaj felled Morten Hjulmand inside the area, leading to referee Fabio Maresca pointing to the penalty spot.
Gabriel Strefezza stepped up, looking to score his 10th goal of the season, but saw his low drive from 12 yards go agonisingly wide of the left post.
That miss would be punished just 11 minutes later when Luis Alberto released a through ball into Ciro Immobile’s path for the Italian marksman to calmly net the opener, just as he did in the reverse fixture.
The visitors responded in style though and retaliated in first-half stoppage time as Oudin venomously struck into the bottom corner to leave Lazio boss Sarri fuming with the scores level at the interval.
In superb fashion, Marco Baroni’s outfit completed the turnaround and took the lead just six minutes after the restart thanks to a fantastic first-time finish by Oudin yet again, following a slick pass from Strefezza.
Now staring at what would be a first win in six visits to the Italian capital, Lecce looked to hold firm against a Lazio side eager to overturn their poor results of late.
Pressure mounted as the clock ticked ever closer to full-time, and Lecce hearts were in mouths when Pedro's effort cannoned back off the woodwork.
Just as it appeared the visitors would see out a third successive victory over Lazio, a mishap at the back allowed Milinkovic-Savic to slide home a dramatic last-gasp leveller that keeps his side in control of their top-four fate.
Lecce, albeit disappointed by seeing their win go up in smoke in the dying seconds, moved five points clear of the relegation zone, while Lazio sit four points clear of the chasing pack inside the Champions League places having played before all of their rivals.
Flashscore Man of the Match: Remi Oudin (Lecce)
