Luke Garbutt’s penalty had put the visitors ahead in the first half, but in a second 45 minutes that belonged to the Foxes, Hopper finally struck on the hour mark with a looping shot to level the scores.
The Toffees then hit the post and Sean St Ledger, who played the full 90 minutes, went close with a volley, but neither side could force a winner – meaning the Foxes are one step closer to a top half finish.
City are now six unbeaten in the league with two games left to play, and afterwards, manager Steve Beaglehole reflected: “I’m pleased with a point. At half time if you’d have said we’d pull it back I’d have taken it. It keeps our good run going and you can’t win every game, it’s just impossible.
“I thought they were better than us in the first half. We’d heard a lot about them and I don’t think they get mentioned enough as a club for their youth development and the players they’ve brought through.
“It was a good performance against a good team. We had one or two stern words at half time and in the second half we were by far the best side. We scored, created chances and were unfortunate not to score more than one.”
The in-form Foxes named an attacking line-up for the fixture, but were soon given an early indication of just what the Toffees were capable of – Chris Long three times breaking from midfield to try his luck – however none of his efforts found the target.
At the other end a great left foot delivery from Callum Elder almost caused the visitors problems, but thankfully for them, Hopper’s header ballooned over the crossbar.
It was a closely fought encounter, but with just under 20 minutes played, the visitors got their noses in front from the penalty spot after George Taft was judged to have brought down Conor Grant.
Garbutt stepped up to the mark and fired a simply unstoppable left footed strike down the middle of the goal to make it 1-0.
Both Long and Joe Dodoo then shared almost identical chances at either end – powerful low left footed drives from close range – but the goalkeepers were equal to the challenge.
After the break Taft made way for Alie Sesay, meaning Kieran Kennedy reverted to centre back alongside St Ledger, but it was the same story for the Foxes, who despite putting some high quality deliveries into the box, couldn’t find a way through.
City were controlling possession however, and after a huge spell of pressure came within a whisker of an equaliser on 56 minutes – Harry Panayiotou’s glancing header from Cain’s cross clawed off the line by a scrambling Jindrich Stanek.
The pressure finally paid just before the hour mark. A ball into the box was only half cleared, allowing Blyth to head back into the area for Hopper, who facing away from goal, produced an unorthodox finish that looped over Stanek to level.
At other end, City had Logan to thank for pulling off an incredible save with his feet to deny Grant a goal from 12 yards after St Ledger had blocked Long’s initial effort.
With 20 minutes left, Hopper’s knockdown found St Ledger in the box, but Panayiotou couldn’t get out of the way of the Republic of Ireland international’s volley in time and Everton were let off the hook.
Again though, the game opened up with chances for both sides – Panayiotou testing Stanek with a rising drive, while Everton substitute Courtney Duffus struck the base of the post from 20 yards after a Joe Williams lay-off.
Cain followed that up with two fine efforts from range – one on his left and one on his right – however both were tipped around the post by a full stretch Stanek.
Marcel Barrington then dragged one final effort wide of the post as the Foxes were made to settle for a point after a thoroughly entertaining 90 minutes of football.
CITY (4-4-2): Logan, Kennedy, Elder, Watson, St Ledger, Taft (Sesay 46), Panayiotou, Cain, Blyth (Barrington 75), Hopper, Dodoo (Dawson 64)
SUBS NOT USED: Smith, McCourt
GOAL: Hopper 59
EVERTON (4-3-3): Stanek, Jones, Garbutt, Ledson (Duffus 63), Langton, Browning, Williams, Grant, Gueye (Dyson 90), Long, Green (Kenney 75)
SUBS NOT USED: Taudul, Touray
GOAL: Garbutt pen 19
REFEREE: Ian Dudley