Salah grabbed his first goal in London since May 2018 with a penalty and Oxlade-Chamberlain struck after the break as the Reds continued their inexorable march towards the title.
Jurgen Klopp's side were not at their devastating best, but they did not have to be to make it 23 wins from 24 matches and stay on course for a 19th league title, and a first for 30 years.
West Ham needed points for very different reasons but they are low on confidence, and numbers, at the moment.
Nevertheless David Moyes' men will host Brighton on Saturday heartened by the fact they were not on the end of the battering many expected.
The Hammers youngster was not backwards in coming forwards, though, and two delightful passes almost put Sebastien Haller in on goal only for Joe Gomez and then goalkeeper Alisson Becker to get there first.
West Ham held out until 10 minutes before half-time, when a scramble in the penalty area ended with Diop bundling over Origi.
VAR had a good look at a replay of Roberto Firmino's hand potentially brushing the ball in the build-up, but the spot-kick was confirmed and Salah thumped it home for his first goal in the capital since he netted at Crystal Palace 22 months ago.
It was by no means Liverpool at full throttle and they should have been pegged back after the break when Declan Rice's cross found Manuel Lanzini eight yards out, but the Argentinian mis-kicked wildly.
The Reds broke down the other end and Fabianski had to keep out Firmino's close-range effort at full stretch.
But Fabianski was powerless to prevent Oxlade-Chamberlain doubling Liverpool's lead seven minutes after the break.
To their credit West Ham's heads did not drop like they have in the recent past and Rice forced two excellent saves from Alisson, with Trent Alexander-Arnold putting the rebound from the first against a post.
Salah also struck the woodwork late on and Fabianski saved from Naby Keita but West Ham just about kept the visitors at bay.
It may be a small crumb of comfort but, while Liverpool disappear into the distance at the top, the hosts did at least avoid the four-goal defeat which would have seen them drop into the bottom three.