Marek Hamsik shone for Jan Kozak's side as they moved level on points with Wales ahead of the latter's crunch clash with England, while Russia languish bottom of Group B and must win against Chris Coleman's side on June 20 if they harbour any hopes of progressing.
Slovakia had only scored once in their past four meetings with Russia but thanks to the superb Hamsik and Russia's ailing back four, they ran riot in a lively first half under the Stade Pierre-Mauroy roof.
It was Hamsik's pass that freed Vladimir Weiss to fire home the opener after half an hour before smashing home Slovakia's second on the stroke of half-time.
And though Denis Glushakov's late goal gave the Russians hope, they could not repeat Saturday's last-gasp heroics.
Kozak's men needed a win to retain any realistic chance of emerging from Group B and started brightly, Napoli's Marek Hamsik lashing just over from 30 yards with just over ten minutes gone.
With half an hour gone, Weiss made the most of some suspect Igor Smolnikov defending to open the scoring, latching onto a superb Hamsik pass before cutting back inside and firing past a helpless Igor Akinfeev.
It was Hamsik who continued to shine brightest in Lille, striking a hammer-blow to Russian hopes just before half-time with a sensational curling effort that left Akinfeev helpless before ricocheting off the post into the back of the Russian net.
Slutski obviously delivered a rocket at half-time as the Russians looked far more lively after half-time and Fedor Smolov had a powerful shot blocked, with Denis Glushakov missing the rebound.
Glushakov set up a frenetic end when he headed home Oleg Shatov's cross with ten minutes remaining, but Slovakia were able to hold out.
Weiss 32, Hamsik 45
Referee: Damir Skomina 6/10
Match rating: 3/5
Star man: Marek Hamsi (Slovakia)
Russia: (4-2-3-1): Akinfeev 5, Smolnikov 4, Schennikov 5, Ignashevich 5, V. Berezutski 4, Neustadter 5 (Glushakov 45 7) , Golovin 5 (Mamaev 45 6), Kokorin 6 (Shirokov 76 6) 6(Shirokov 76 6), Shatov 6, Smolov 6, Dzyub 6
Slovakia: (4-3-3): Kozacik 6, Pekarík 7, Skrtel 7, Durica 7, Hubocan 7, Pecovsky 6, Kucka, Hamsik 9, Mak 7 (Duris 80 5), Weiss 8 (Svento 72 6) Duda 7 (Nemec 69 6)