Fulham let slip a two-goal lead to draw 2-2 at home to west London rivals Queens Park Rangers while Villa suffered a second loss in a week, going down 1-0 at struggling Bolton Wanderers.
Leaders Wolverhampton Wanderers will soon be celebrating their return to the top flight after a 3-1 defeat of Burton Albion moved them six points clear of second-placed Cardiff City and 13 ahead of third-placed Fulham.
Only the top two go up automatically.
Fulham set a new club record of 16 league games undefeated but were kicking themselves after surrendering a two-goal lead at Craven Cottage.
Goals by Tom Cairney and Lucas Piazon put them in control but QPR replied in first-half stoppage time through Massimo Luongo's volley before Pawel Wszolek levelled after the break.
They are seven points behind in-form Cardiff, who face playoff hopefuls Derby County on Sunday chasing an eighth successive league win.
"We cannot be satisfied. I am not here to fight for records, I am here to win the games," said Fulham manager Slavisa Jokanovic. "We didn't win. I cannot be satisfied.
"We had it under control, but the first goal they scored caused important damage."
Villa beat Wolves last weekend but then lost at home to QPR and slumped again against Bolton, who moved six points clear of the bottom three thanks to Adam Le Fondre's goal.
Third-from-bottom Birmingham City's survival hopes got a lift as they beat Hull City 3-0 but bottom club Sunderland are losing touch after a 2-0 home defeat by Preston North End.
"We're only one win away from changing it round but you'd write us off because we keep making mistakes and we're not rising to the challenge," manager Chris Coleman said.
Preston are now only two points off Middlesbrough, who occupy the last of the promotion playoff spots.
Boro drew 1-1 with Brentford.
(Reporting by Martyn Herman; Editing by Ken Ferris, Neville Dalton)
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