Mikel Arteta’s men become the first side to ever win three consecutive away games in the English top-flight by five or more goals.
By contrast, Sheffield United also set a new record by becoming the first English top-flight side to concede five or more goals in three straight home matches.
Arsenal’s stunning streak of 31 goals in seven consecutive Premier League wins since a winter break has at least built up a big advantage over their rivals should the title be decided on goal difference.
They remain in third, just two points behind leaders Liverpool and one adrift of defending champions City.
However, Arteta’s men can go top with victory at home to Brentford on Saturday ahead of Sunday’s showdown between Liverpool and City at Anfield.
There appeared little doubt over the outcome from the first whistle at Bramall Lane.
Bukayo Saka rattled the crossbar after just two minutes and what little resistence there was from the Blades ended just five minutes in.
Rice’s cross picked out the unmarked Odegaard to turn into the bottom corner.
Saka’s five-game scoring streak in the league came to an end but he did bag two assists before going off at half-time.
The England international turned former Arsenal defender Austin Trusty with ease as he got to the by-line and his driven cross flicked off Bogle into his own net.
Martinelli’s deflected effort quickly made it 3-0 and forced United boss Chris Wilder to make a change after just 17 minutes.
Ben Osborn replaced Oliver Norwood but a change of shape did little to stem the bleeding for the hosts.
Havertz is beginning to silence his critics after a slow start to life at the Emirates after a £65 million ($82 million) move from Chelsea.
The German international slammed home on his left foot for Arsenal’s fourth.
Rice then got in on the party by sweeping home Saka’s cross six minutes before half-time.
Saka was handed a rare rest for the second period and only the sight of Martinelli hobbling off just after the hour mark blighted a perfect night for the visitors.
White rounded off the scoring with a cool finish from Havertz’s cut-back on 58 minutes as Arsenal matched their record Premier League away win, set just last month at West Ham.
By that stage many of the home support had headed for the exits, resigned to their side’s fate on the night and the season.
Wilder’s men remain rooted to the foot of the table, 11 points adrift of safety with 11 games remaining.
Arsenal on the other hand are 11 matches away from a first league title for 20 years and could not wish to be in finer form heading down the home straight.
© Agence France-Presse
Photo: Twitter @StatmanDave