The young Reds dominated the vast majority of Wednesday’s Group C match at St Helens, but missed a litany of chances before Dejan Joveljic gave the visitors the lead against the run of play with 15 minutes remaining.
Plenty of late drama was still to come, though.
Liverpool captain Adam Lewis saw a penalty saved by Milos Gordic before Rafael Camacho drew the hosts level with a brilliant curling effort five minutes from time.
Barry Lewtas’ team refused to settle for a point, however, and Williams’ towering header from Lewis’ corner earned all three.
And with Paris Saint-Germain and Napoli drawing 0-0 in the French capital, the young Reds now sit three points clear at the top of the pool.