Hamilton top of the pile after second practice at Italian GP
Seven-time world champion Hamilton clocked a fastest lap of one minute, 20.738 seconds at Monza, just 0.003 seconds ahead of McLaren's Norris who is the closest challenger to Max Verstappen's current F1 supremacy.
Norris trails Red Bull's championship leader by 70 points in the drivers' championship after a stunning win at last weekend's Dutch GP.
That was the fifth straight race not to be won by Verstappen, who was fastest in Friday's first practice session but was 0.872 seconds behind Hamilton in the second back in 14th place.
Hamilton's display in a session disrupted for over 10 minutes by Kevin Magnussen crashing his Haas at the Lesmo corners is a good sign for the rest of the weekend, as he has won two of the last four GPs and is racing at the home track of his future team Ferrari.
The 39-year-old will join the Scuderia next season, replacing Carlos Sainz who was third in the second session, 0.103 off the pace.
Hamilton's current teammate at Mercedes George Russell finished the session 0.348sec back in sixth, a decent result after his car was badly damaged by rookie Andrea Kimi Antonelli earlier in the day.
Italian Antonelli's first-ever F1 drive ended quickly and in spectacular fashion early in the first practice session as he spun off the track with just four completed laps under his belt.
The 18-year-old was given a chance by Mercedes to drive Russell's car but lost control at the Parabolica and smashed into the trackside barriers, seriously damaging the front end.
Antonelli said sorry as he climbed out unhurt, and Mercedes called the incident "unfortunate but all part of the learning curve".
"He apologised first of all, and that is what you need to do when you bring a car back that looks a little bit like a Lego box falling on the floor," said team chief Toto Wolff.
Wolff was unperturbed by the crash, saying that "no one's interested in FP1 anyway" and adding that the Italian would get probably another chance in a Mercedes F1 car at the Mexican GP at the end of October.
Antonelli, who competes in the Formula Two championship for Prema Racing, is reported to be in contention to be Russell's teammate when Hamilton switches to Ferrari.
He was not the only driver to have problems at the Parabolica as Sainz nearly slid off and Franco Colapinto, another rookie who has replaced Logan Sargeant at Williams, hit the gravel at the same corner but managed to get his car back on the track.
On Thursday the same corner even claimed the safety car, suggesting that there could be more problems at that point of the resurfaced, and roasting hot track, over the weekend.
