Southgate and his players need every boost to morale they can get after another night of toil and it came in news from elsewhere in Euro 2024.
Hosts Germany, France, Spain and Portugal are out of sight for now in the other half of the draw, although England will need to lift performance levels markedly to cash in on this slice of good fortune.
If England hoped to produce a performance to answer their critics, this was not it as they were once again lightweight as an attacking force.
They struggled to find a way through Slovenia’s well-drilled and determined defence, backed up by their outstanding goalkeeper Jan Oblak, even when the answer was obvious and came in a moment which actually brought disappointment.
Saka’s goal was disallowed for offside after 20 minutes but it was at least the product of slick, quick passing between Rice and Phil Foden to get in behind Slovenia.
It was the way forward but England simply did not, or could not, exploit it. It was a better display after the break but Southgate’s side once again lacked punch, as they have done against Serbia and Denmark.
Jude Bellingham, the hero of the opening game win against Serbia, once again looked out of sorts and let his frustrations get the better of him with some negative first-half body language.
England will hope for much more from their great young hope as they enter the knockout stage.
They are through – but many questions are left for Southgate to answer.