The England lock scored two tries in 11 minutes to help the three-time European champions progress from Pool One.
Scrum-half Ivan van Zyl, flanker Juan Martin Gonzalez and wing Lucio Cinti also claimed touchdowns at the StoneX Stadium, with Owen Farrell kicking four conversions and two penalties.
Lyon, without an away win in all competitions for almost a year, led by 12 points at half-time.
Centre Josiah Maraku collected a try double and wing Davit Niniashvili also scored, while Lyon skipper Leo Berdeu booted a penalty and three conversions, but Saracens ultimately avoided making a first pool-stage exit since 2011.
Saracens were immediately into their stride, putting together impressive phase-play, and they went ahead after just four minutes.
England forwards Itoje and Ben Earl set up a strong attacking position, and Van Zyl took a quick penalty to cross unopposed.
Victories for Lyon over Bristol and the Bulls meant they arrived in north London having already qualified, but they stunned Saracens through an opportunist 15th-minute score.
Saracens were on the attack, but Van Zyl's pass was intercepted by Lyon's Georgia international wing Niniashvili, who sprinted 80 metres to claim a try that Berdeu converted.
Berdeu extended Lyon's lead with a 26th-minute penalty, and Saracens' initial promise had evaporated as the visitors began to assert control.
Lyon displayed composure and accuracy in attack, and it was no surprise when they extended their lead just before half-time.
Saracens found themselves in a prolonged defensive mode, with Lyon patiently creating an opportunity to strike, with Maraku touching down and Berdeu converting for a 17-5 interval lead.
Lyon were good value for their advantage, but it was cut by seven points early in the second period when Itoje pounced for a try that Farrell converted.
Just when Saracens looked like they might have some much-needed momentum, they were undone when Farrell twice had kicks charged down in rapid succession.
Lyon prop Jerome Rey blocked the first attempted clearance, then lock Joel Kpoku replicated it and Maraku gathered the bounce for his second try. Berdeu's conversion made it 24-12 before Farrell kicked a short-range penalty.
And when Saracens decided to go route-one, it was rewarded as Itoje collected his second try, this time from a lineout drive, and Farrell's conversion left his team just two points behind.
The fly-half then kicked another penalty as Saracens edged in front, before Gonzalez's score finally ended an impressive Lyon challenge and Cinti added try number five.