The Toffees can make up ground in the race for a top-four spot on Sunday when they visit White Hart Lane against a Spurs side facing injury worries after Europa League action
The Toffees are currently four points adrift of Chelsea in fourth in the hunt for Champions League football and, after Spurs' exertions against Basel during their 2-2 draw in the Europa League quarter-finals, their old servant feels that there is an opportunity to narrow the gap.
Spurs lost Gareth Bale, William Gallas and Aaron Lennon to injury against the Swiss side, although Everton will be without Steven Pienaar and Marouane Fellaini through suspension.
Stuart told talkSPORT: "It's going to have to be a big afternoon for the Toffees because Tottenham are in some decent form.
"They've got a tough game of their own against Basel so hopefully they will be struggling a little bit leg-wise on Sunday and Everton can take advantage.
"Irrespective of what happens, Everton have had another terrific season."