The Premier League leaders were forced to dig deep yet again on Saturday in the process of securing a 12th victory in 13 outings so far this season.
After a scrappy opening half in south London, a prodded finish from Sadio Mane edged the Reds ahead, but Wilfried Zaha struck back for the hosts in the final 10 minutes.
There was parity for a matter of moments, however. Roberto Firmino capitalised on a scramble from a corner to sweep in a second – winning – goal for the visitors.
Alexander-Arnold considered the satisfaction the players felt after the final whistle a symbol of how hard they had to work for their three points.