Patrick Bamford, Kike and Jelle Vossen all found the net for Boro, while Derby lost for the second time in a row as Dale Stephens and Kazenga Lualua struck for Brighton.
Watford are third after a 1-0 home win over Fulham, while Bournemouth are two points and a place behind after they defeated Wolves 2-1.
Sixth-placed Brentford trounced Huddersfield Town 4-1, while Charlton Athletic and Cardiff City both won and Bolton Wanderers drew 1-1 at home to Reading.
In League One, Bristol City took another step towards the title by moving 10 points clear with a 3-1 success at Leyton Orient.
Luke Freeman, Aden Flint and Aaron Wilbraham were the goalscorers for City, who took advantage of Preston North End's 2-2 draw at home to Doncaster Rovers.
MK Dons and Swindon Town both failed to overtake Preston and move into second, as they went down 2-1 at home to Chesterfield and 3-0 at home to Gillingham respectively.
The division's bottom three clubs - Yeovil Town, Crawley Town and Colchester United - all lost by one goal to nil, against Walsall, Bradford City and Notts County.
Peterborough United, Barnsley, Oldham Athletic and Rochdale were the other winners in League One, while Fleetwood Town and Scunthorpe United drew 2-2.
In League Two, Shrewsbury Town moved back to the summit on goal difference with a 2-1 victory at Accrington Stanley thanks to a brace from Bobby Grant, with previous leaders Burton Albion not in action.
Wycombe Wanderers are just a point behind in the final automatic promotion place after Paul Hayes and Fred Onyedinma earned a 2-1 victory at Tranmere Rovers.
Bury prevailed 1-0 over fellow high-fliers Luton Town, while Southend United drew 0-0 at AFC Wimbledon and Newport County suffered a 1-0 home loss at the hands of Mansfield Town.
Bottom club Hartlepool United lost 2-0 at Dagenham and Redbridge and second-from-bottom Cheltenham Town went down 1-0 at Carlisle United.
Elsewhere, there were wins for York City, Northampton Town and Stevenage, while Oxford United drew 1-1 with Morecambe.
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