City and United, currently first and second in the Premier League, took contrasting routes to the last 16, where they were joined by Chelsea, Arsenal and Everton as the big guns advanced despite fielding weakened teams.
United manager Jose Mourinho made nine changes from the side that thrashed Everton on Sunday, with Rashford and Juan Mata the only survivors.
Rashford took just five minutes to open the scoring with a deft finish and the England forward struck again in the 17th minute with a powerful effort.
Burton, 19th in the Championship, were killed off in the 36th minute when Jesse Lingard’s shot deflected in off Ben Turner.
Injury-ravaged United left-back Luke Shaw came on for his first appearance since April before Anthony Martial scored the fourth from Rashford’s pass on the hour.
Lloyd Dyer got one back for Burton in stoppage-time.
At the Hawthorns, City boss Pep Guardiola made eight changes from the 6-0 demolition of Watford, giving Yaya Toure his first start of the season, while Ilkay Gundogan, back from a serious knee injury, started for the first time since December.
It was from Gundogan’s saved shot that Leroy Sane slotted in City’s third minute opener.
But, casting a shadow over City’s progress, Gundogan was forced off with a knock in the second half.
Claudio Yacob equalised for Albion with a close-range finish in the 72nd minute, only for Germany winger Sane to produce a superb curling winner five minutes later.
Michy Batshuayi’s hat-trick helped Chelsea crush second tier Nottingham Forest 5-1 at Stamford Bridge.
Antonio Conte made nine changes from Sunday’s 0-0 draw against Arsenal, with Eden Hazard given his first start of the season after recovering from ankle surgery.
Kenedy was starting for the first time since being sent home from Chelsea’s pre-season tour of Asia in July following his offensive social media comments about China.
– Batshuayi shines –
Chelsea’s Michy Batshuayi (R) scores his second and the team’s fourth goal during their match against Nottingham Forest at Stamford Bridge in London on September 20, 2017
His bid to get back in Conte’s good books got underway when the Brazilian winger put Chelsea ahead in the 13th minute with his first goal since March 2016.
Batshuayi’s close-range finish doubled Chelsea’s lead six minutes later before 20-year-old Belgian Charly Musonda smashed in his first Blues goal in the 40th minute.
Batshuayi got his second from Hazard’s pass in the 53rd minute and the Belgian striker completed his treble four minutes from full-time, with Forest replying through Tendayi Darikwa in the closing moments.
A week after his 17th birthday, substitute Ethan Ampadu became the first player born this millennium to represent Chelsea.
Theo Walcott sealed Arsenal’s 1-0 win over third tier Doncaster at the Emirates Stadium.
Gunners boss Arsene Wenger changed his entire line-up from the Chelsea draw, with Per Mertesacker, Alexis Sanchez and Olivier Giroud among the starters.
Sanchez set up the 25th minute opener, clipping a fine pass to Walcott, who controlled well before slotting home.
Dominic Calvert-Lewin blasted Everton to a 3-0 victory over second tier Sunderland at Goodison Park.
With eight changes from their defeat at United, Ronald Koeman’s side went ahead in the 38th minute as Calvert-Lewin claimed their first goal since August 24.
Calvert-Lewin netted again in the 51st minute and in the 83rd minute Oumar Niasse grabbed his first Everton goal since his 2016 move from Lokomotiv Moscow.
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