Erik Lamela ensured Tottenham stays at the top of Group J and moves on to the knockout stages with a hat-trick.
The Argentine led the English side to a 4-1 win over Monaco without any help from Harry Kane, Dele Alli and Christian Eriksen.
Tottenham would extend their winning streak to a total of nine games, with just 2 defeats in their last 21 matches.
Lamela scored with three past Monaco keeper Danijel Subasic, but the Croatian will feel he was beaten far too easily at his near post.
However, the best goal of the night was a cool finish applied by Carroll after his quick feet had left Elderson wrong-footed.
Nabil Bentaleb and Nacer Chadli continued their recoveries from injury with tidy substitute performances, while 18-year-old Joshua Onomah impressed in his first senior start.
The midfielder combined some probing passing with clever runs and he might have scored, but he opted for precision rather than power from six yards out.
Meanwhile, all was quiet at the Tourbillon Stadium as Sion held down Liverpool to an uneventful goaless draw.
Divock Origi had the best chances for goal, but a mistimed volley in the first half and a fine last-ditch tackle stopped the Belgian.
Meanwhile, Reds keeper Simon Mignolet was forced to make a save to deny Sion’s Ebenezer Assifuah.
Although their unbeaten record in the championship remains intact, Liverpool players were clearly left frustrated, having a lot less to celebrate compared to the jubilant Swiss team.
The draw notwithstanding, the spiritual leader of the Reds appeared to be happy enough. Jurgen Klopp was “thrilled” that none of his players was hurt.
The German said: “The ground was very difficult to play and for both teams the first thing to do was show you were prepared for a game like this and that is what my team did.”
“We saw the pitch and we knew what can happen on a pitch like this but as a professional footballer and especially as a manager you cannot talk about the pitch.”
“I am really satisfied, no-one is injured and they were very focused and concentrated on the game.”
Both Sion and Liverpool are through the round of 32, where they may go up against clubs such as Manchester united depending on Monday’s draw.