But Felix Platte levelled with a header on 70 minutes as England were forced to battle to extend the match to extra-time and potentially penalties.
Redmond, captain James Ward-Prowse, Alfie Mawson and Jordan Pickford all age out now with new faces needing to step into their shoes. In most other circumstances, England vs Germany could easily be the championship match, but the fact that we get to watch these two colossal global squads go head-to-head in the semi-finals will surely be a treat.
England duo Nathaniel Chalobah and Nathan Redmond came off with injuries against Poland.
But, the spectre of Germany in a semi-final of a major tournament will be well known to England fans.
Selke went down but referee Gediminas Mazeika turned down his appeals.
The young German shot stopper has been superb throughout this tournament and certainly limited the damage last time out against Italy where he made three goal-saving parries.
The high tempo start was in contrast to a limp atmosphere within the Tychy Stadium but England were on top and blew another fine opening when Abraham headed straight at Pollersbeck.
One-time Arsenal forward Serge Gnabry has enjoyed a productive tournament on the left of the front line, while Maximilian Arnold, Mahmoud Dahoud and Tottenham-target Max Meyer comprise the most talented midfield trio in the tournament.
It will be hard to get over the penalty defeat immediately but England are stronger than they were in 2015, when they exited at the group stages, and will recover.
Stefan Kuntz's side has picked it self so far in the tournament but the former Germany global could make changes after defeat to Italy in the final group game.
The Hoffenheim defender advanced into the area and picked out the ideal cross for Selke to power in from 10 yards.
England have reached the knockout stages of this tournament for the first time since 2009 courtesy of two wins and a draw from their three Group A fixtures.
They were on the ropes but landed their own sucker punch four minutes before the break to equalise.
The Chelsea midfielder was unmarked six yards out but planted his header over the bar.
England's mental strength had prevailed and they grew stronger still when Abraham fired them ahead five minutes into the second half.
But Germany always looked a threat and Platte - on for the injured Selke - expertly guided a header past Pickford to level.
Platte appeared to have struck the winning goal on 79 minutes, but he was deemed to be offside, which looked a marginal call from a linesman.
Germany dominated as England were prepared to defend after getting their goals. How has Amiri managed to miss that?
But Abraham could not capitalise on the advantage and hit a terribly soft penalty down to Pollersbeck's right, which was easily saved.