Salah rolled the ball behind him with a back-heel, with Alexander-Arnold running on to it and lashing home a stunning effort past Chelsea goalkeeper Kepa Arrizabalaga.
The visitors doubled their lead mid-way through the first-half as Alexander-Arnold was further involved in another set-piece. The youngster played a similar back-heel pass to Andy Robertson, who whipped in the ball for Roberto Firmino to nod in.
The Reds always looked a threat from set-pieces against Frank Lampard's side, with Klopp putting the success of their routines down to Liverpool assistant manager Krawietz.
“It's of course from the training ground, the Robbo (Robertson) one is from the training ground," added Klopp. “The Trent one, I really see the boys on the pitch today had the best view on the pitch. It's their job to see the best opportunity to score.
“It was a direct free-kick so could have scored directly, but this little move changed the whole angle and made it pretty impossible for Kepa (Arrizabalaga) to make a save. It was a brilliant goal.
“Pete Krawietz and our analysts, they do a really good job around set-pieces, especially corner kicks. I loved the corners in the second half where we probably should have scored twice.
“But it wasn't a set-piece game, we played a lot of good stuff and in the end you have to score and that's what we did. All good."
Klopp's side are back in action in midweek as they travel to MK Dons in the League Cup on Wednesday night.
The likes of Adam Lallana, Alex Oxlade-Chamberlain, James Milner, Joe Gomez and Xherdan Shaqiri could come in to the side as the boss seeks to rest some of his players amidst a busy spell in their schedule.
Rhian Brewster is another who is likely be involved in some capacity, with the youngster featuring on the substitutes bench at Stamford Bridge on Sunday.
At least one of the usual attacking trio of Salah, Roberto Firmino and Sadio Mane could be rested, giving Brewster the chance to make his debut against the League One side.