Yet they could not add a second goal when they were on top and the game swung in Croatia’s favour once Ivan Perisic had scored an improvisational equaliser in the 68th minute, showing great determination to beat Trippier and Kyle Walker to a cross from the right and twisting mid-air to turn an awkward volley, almost head-height, past Jordan Pickford.
related discussion: die Hereingabe - cross (in soccer)
Comment on the same goal by Barney Ronay, the Guardian's remarkably literate sportswriter.
"Cross" is the standard word. In UK match commentary, etc., you would also hear it described it as a "ball in":
X played a lovely ball in from the right.
Y met the ball in from X with a glancing header.
This is essentially short for "a ball into the box".
Edit: What #2 calls a "flache Flanke" would be a "low cross" in English. Unless it actually rolls along the grass, it would still count as a "cross" to me.