Armed with a commanding advantage from last week’s tie in Milan, the Rossoneri knew the pressure was on the hosts in the early stages as they looked to overturn a sizable deficit. It was Milan, however, who came close to a breakthrough inside two minutes when Rafael Leao saw a low effort thwarted by the legs of Steve Mandanda.
Grateful for that reprieve, Rennes settled into the match and the hosts soon took the lead, as Bourigeaud rifled a strike into the bottom corner from the edge of the box.
Undeterred by that setback, Milan remained a threat in the final third, and their attacking intent was rewarded with an equaliser in the 22nd minute when Luka Jovic headed home from a clever Theo Hernandez delivery.
The frantic nature of the contest continued as the first half progressed, and Mike Maignan had to be alert to turn Arnaud Kalimuendo’s sharp effort over the bar, keeping the visitors on level terms at the break.
Determined to find a quick-fire goal at the start of the second period, Rennes were handed a golden opportunity to do so when Simon Kjaer was penalised for a clumsy foul on Martin Terrier in the box.
Bourigeaud assumed the responsibility from the spot and the French midfielder tucked the resulting penalty beyond the reach of Maignan.
Similar to the first half, Milan found a swift response just four minutes later through the dangerous Leao, who raced past a couple of Rennes defenders before finishing coolly beyond Mandanda.
The end-to-end action continued heading into the final half-hour, and Bourigeaud completed his hat-trick with a second penalty of the evening after Jovic was harshly adjudged to have handled Kalimuendo’s goal-bound header.
That gave the hosts a late lifeline, but despite plenty of pressure and a couple of half-chances, the Milan rearguard held firm during the closing stages to book their place in Friday’s last-16 draw.
Flashscore Man of the Match: Benjamin Bourigeaud (Rennes)
Other early Europa League results:
Freiburg 3-2 Lens AET (Freiburg progress on aggregate)
Qarabag 2-3 Braga AET (Qarabag progress on aggregate)
Toulouse 0-0 Benfica (Benfica progress on aggregate)