The BBC One show - with guests including the cast of Anchorman 2, Monty Python and Jackie and Joan Collins - was watched by over 200k more viewers than last year's edition, which became Norton's highest rating show of his 2012 series.
The channel continued its ratings success with Gary Barlow's Big Ben Bash Live entertaining 6.76m (38.4%) in the run up to midnight. 13.7m (67.5%) welcomed 2014 with BBC One's New Year Live, an impressive 3m increase on last year's celebrations.
Earlier in the night, 3.87m (10.5%) tuned in to Celebrity Mastermind at 7pm, while 3m (15.4%) watched Two Doors Down at 9pm.
Over on BBC Two, 2.56m (18.6%) saw in the New Year with Jools Holland's Annual Hootenanny 2013 from 11.30pm. Earlier at 7.30pm, a festive Christmas University Challenge quizzed 2.41m (11.5%), while new series Nature's Weirdest Events kicked off with 2.22 (11%) at 8pm.
Tudor Monastery Farm attracted 1.57m (8.06%) at 9pm and the last episode in the current series of Mock the Week gathered 1.07m (5.74%) at 10pm.
On ITV, 2008 ABBA musical Mamma Mia entertained 2.13m (10.82%) at 8pm, followed by a look back at the most humorous moments of the last year with 2013: A Funny Old Year amusing 1.46m (8.15%) at 10.15pm.
Over on Channel 4, 1.54m (8.19%) celebrated with Alan Carr's New Year Specstacular at 9pm, with guests including Strictly Come Dancing champion Abbey Clancy, Emma Willis and Keith Lemon.
Earlier, Deal or No Deal attracted 900k (4.26%) at 7pm, while Celebrity Fifteen to One was watched by 1.53m (7.55%) at 8pm.
Channel 5's The Gadget Show impressed 649k (3.08%) at 7pm, 1.18m (5.87%) tuned in to World's Strongest Man at 8pm and the Greatest Stand Up Comedians countdown brought in 1m (5.44%) at 9pm.
Meanwhile, ITV3 scored the highest primetime ratings on the multichannels, with Midsomer Murders entertaining 995k (5.01%) at 8pm. 515k (2.82%) tuned in to Agatha Christie's Poirot directly afterwards at 10pm.
BBC Three attracted 747k (3.76%) at 8pm with a showing of Indiana Jones and the Temple of Doom.
BARB ratings data supplied by Attentional