England began on the front foot and Lallana’s stinging half-volley, which came about after an enterprising run forward from Kyle Walker, forced Igor Akinfeev into a smart save seven minutes in.
Rooney was being afforded the freedom of the Velodrome from his deeper position, and the England skipper started a move that ended with Dele Alli glancing Sterling’s inswinging cross from the left wide, with Kane just unable to make contact behind him.
Russia were struggling to get out of their own half, and another two England chances went begging in the opening 20 minutes.
First, Alli failed to anticipate Danny Rose’s dangerous low delivery from the left that would have left him with a tap-in, before Lallana dragged a shot wide after more good work from Walker.
Kane then finally had the ball in the net only to be correctly denied by the offside flag, before Rooney – advancing forward for the first time – fizzed an effort from 20 yards straight at Akinfeev.
Half-time came at the wrong time for a relentless England side, and they struggled to move back through the gears after the interval.
Russia looked increasingly comfortable as England’s intensity dropped, and Fyodor Smolov had Joe Hart scrambling when he attempted to curl an effort into the bottom corner just after the hour.
Slutsky had his goalkeeper to thank for keeping his team level in the 70th minute. Danny Rose’s low cross was only half-cleared to the onrushing Rooney, who tried to place a low effort into the corner only to be denied by a stunning one-handed stop from Akinfeev.
But there was nothing Akinfeev could do moments later, when Dier finally broke the deadlock in some style.
It appeared as if Kane would strike the free-kick from just outside the box, but he ran over the ball to allow his Tottenham team-mate to thump an unstoppable, side-footed drive into the top corner.
Dier’s goal was no more than England deserved, but they were made to pay for their lack of ruthlessness when skipper Berezutski rose highest to nod back across goal and in.