Meanwhile, former Premier League star Demba Ba returned to England to grab a late leveller for Besiktas at Tottenham while Celtic edged Dinamo Zagreb 1-0.
Cameroonian striker Eto’o cancelled out Ari’s first-half opener for Krasnodar to earn Roberto Martinez’s men some reward from their journey of almost two and a half thousand miles to southern Russia.
The result leaves the Toffees with four points from two matches in Group H after their 4-1 thumping of Wolfsburg a fortnight ago.
Wolfsburg and Lille drew 1-1 in Germany in the other game in the group on Thursday evening, with Belgium midfielder Kevin De Bruyne scoring a wonderful volley to earn the hosts a point after his compatriot Divock Origi, on loan from Liverpool, had put the French side ahead.
Everton face a double-header against Lille next in arguably the toughest group in the competition.
“I am pleased because I thought Krasnodar played very well,” Martinez told ITV.
“They started with a lot of energy but I am very pleased with the manner we stayed in the game. We showed incredible character.”
Martinez has promised to put all his resources into trying to win the Europa League, although he still made five changes to the side that drew 1-1 with Liverpool in last weekend’s Merseyside derby.
Eto’o, Darron Gibson, Aiden McGeady, Christian Atsu and Leon Osman were all handed starts for the meeting with Krasnodar, who started their very first European campaign in the second qualifying round in mid-July.
Krasnodar drew 1-1 in Lille in their opening game and showed their threat with the pace of Colombian Ricardo Laborde particularly dangerous.
Nevertheless, it was the Brazilian Ari, a former team-mate of McGeady at Spartak Moscow, who put Krasnodar ahead two minutes before the break, finishing past Tim Howard after Phil Jagielka had inadvertently helped an Odil Ahmedov ball into his path.
It could have been all over for Everton in the 66th minute when another Brazilian Wanderson, just on as a substitute, weaved his way through in the box and hit the bar from eight yards out.
The visitors rode their luck and the veteran Eto’o brought them level with time starting to run out.
Eto’o, familiar with Russia from his two-year spell with Anzhi Makhachkala, played the ball out to Leighton Baines on the right before continuing his run and connecting with the full-back’s cross from the edge of the six-yard box.
Elsewhere, holders Sevilla came from two goals down to draw 2-2 with Rijeka in Croatia in Group G, Liverpool loanee Iago Aspas getting one back before Stephane Mbia’s stoppage-time equaliser.
Napoli won 2-0 at Slovan Bratislava in Group I thanks to goals from Marek Hamsik and Gonzalo Higuain, while fellow Serie A side Fiorentina beat Dinamo Minsk 3-0 in Belarus.
Tottenham were ahead against Besiktas thanks to Harry Kane’s 27th-minute strike at White Hart Lane.
But the Turks grabbed a deserved point one minute from time when former Chelsea and Newcastle striker Ba converted a penalty awarded after Vlad Chiriches had handled.
Asteras Tripolis beat Partizan Belgrade 2-0 to take top spot in Group C.
“It’s great to get on the scoresheet but we wanted to come away with a win and to concede that late goal is very disappointing,” said Kane.
Celtic are joint top of Group D after Kris Commons scored in the fifth minute to edge Dinamo Zagreb 1-0 in Glasgow.
Italian giants Inter Milan have a perfect record of two wins in two games after a 2-0 win over Qarabag which put them top of Group F.