The Reds had to rely on Alisson's heroics in the second half when they were under the cosh, but managed to secure the three points.
Liverpool played a high defensive line that was exposed time and again by Palace’s agile attackers in the second half.
Alisson, hence, had to be vigilant as he pulled off some brilliant saves in the second half to preserve Liverpool’s fragile 2-1 lead before they scored a late third goal.
Oxlade-Chamberlain called his teammate "world-class" and admitted the goalkeeper saved Liverpool against Crystal Palace:
"Sometimes you get a bit complacent with expecting Ali to make those sort of saves. But he is world-class and moments like that win you games. You do sometimes get used to him doing it and you can’t take that for granted, it’s unbelievable.
"But it's more disappointing from us because of the way we had the game at that point and had it fairly under control, to then have to rely on him and put him under that pressure to pull off those saves - it's a bit sloppy from us and we weren’t happy with that.
"But it's great to have him behind you in case you do [need him], and he saved us there today and was definitely a massive part of the three points. He's brilliant and he keeps doing it so long may it continue," Oxlade-Chamberlain told Liverpoolfc.com.
Liverpool needed to win after Manchester City dropped points on Saturday. Pep Guardiola’s side were held to a 1-1 draw by Southampton.
After dominating the first half Liverpool were under pressure in the second half against Crystal Palace and saw their deficit reduced to 2-1.
Alisson was called into action time and again and made some crucial saves to preserve the Reds’ narrow 2-1 lead. Eventually, Fabinho scored a penalty in the 89th minute to seal the win.
The win was crucial as it helped Liverpool cut down Manchester City's lead at the top of the league table to nine points. The Reds also have a game in hand.