With Brentford having lost 1-0 at Stoke City earlier, thereby crowning Leeds United champion, Fulham responded to move within a point of the top two thanks to two goals from Aleksandar Mitrovic.
Cardiff City swept aside Middlesbrough to keep its play-off ambitions in its own hands, with Preston North End and Millwall now unable to finish in the top six.
At the other end of the table, Stoke's victory sealed its survival, while Kazenga LuaLua struck a huge late blow for Luton Town at Hull City and Charlton Athletic snatched an important point.
FULHAM POUNCES AS BRENTFORD FALTERS
Lee Gregory's first-half finish from close range gave Stoke a 1-0 win over Brentford at bet365 Stadium that ensured its Championship survival and denied the visitors the chance to go second.
Fulham is now just a point behind Brentford in the table after beating Wednesday 5-3 and, with West Bromwich Albion only two above the Cottagers, who will be ready to capitalise on any slip-ups on the final day on Thursday (AEST).
Mitrovic and Neeskens Kebano scored twice at Craven Cottage before Bobby Reid's late fifth, with Jacob Murphy and Atdhe Nuhiu (two) on target for Wednesday, which cannot yet consider itself safe given the risk of a possible points deduction.
BONNE CHANCE FOR LUTON AND CHARLTON
In Sunday's (AEST) relegation showdown between Hull and Luton, it was the visitors that left KCOM Stadium feeling hopeful of survival after LuaLua fired home the winner in the 85th minute.
Luton is now on 48 points, level with Charlton, which was trailing 2-1 to Wigan Athletic until Macauley Bonne equalised on exactly 92 minutes.
Hull is three points behind and, given it is 16 goals worse off than Charlton, it looks destined for League One barring possible points penalties for either Wednesday or Wigan. Bottom-club Barnsley, with two games left, can still stay up.
CARDIFF WIN ENDS PRESTON, MILLWALL HOPES
Two goals from Josh Murphy helped Cardiff to a 3-1 win at Middlesbrough, whose survival could now depend on getting a result on Thursday (AEST), at Wednesday.
Cardiff stays sixth, three points ahead of Swansea City, whose 1-0 win over Bristol City keeps its play-off hopes alive ahead of the final day.
Preston cannot now make the top six, despite beating Birmingham City 2-0 – another side which is not yet guaranteed to avoid the drop – while Millwall is also out of play-off contention after Cardiff's win and its own thrilling 4-3 defeat at Queens Park Rangers.
That was not the day's only seven-goal game: at Ewood Park, Sam Gallagher's 87th-minute header gave Blackburn Rovers a 4-3 win over Reading that lifted Rovers into the top 10.