The towering Dutchman - who recently confirmed that his camp were in talks with Liverpool over his future - scored the visitors' first leveller at the Emirates after a record-breaking goal from Bukayo Saka put Arsenal ahead.
Without William Saliba in the side due to his red-card suspension, the Gunners lacked one of their chief defensive and offensive threats from set-pieces, and Van Dijk capitalised to nod in from a corner.
The 33-year-old's effort preceded another aerial goal from Arsenal new boy Mikel Merino towards the end of the first half, before the visitors got their reward for relentless second-half pressure when Mohamed Salah swept home the leveller.
Salah and Van Dijk's contract situations have dominated the off-field talk at Anfield so far this season, as both men can walk away for nothing when their current deals run out, as can Real Madrid-linked Trent Alexander-Arnold.
Van Dijk gives little away on contract talks
Van Dijk will be able to open pre-contract talks with foreign clubs from January onwards, but speaking to Sky Sports News at full time, the Dutchman affirmed that he was still relaxed about his situation while there is plenty of football to be played.
Asked how he feels about competing at the top level while his contract situation rumbles on in the background, Van Dijk said: "I'm very calm [about my contract situation]. I've said that many times before. Let's see what happens at the end of the season.
"I'm enjoying my football, feeling very good physically and mentally. I feel in a good place. Nothing more can be said. I want to keep enjoying the game, because it's a beautiful game we play."
Van Dijk's equaliser at the Emirates was his first in the Premier League this season, taking his overall record for the Reds to 24 goals and 12 assists from 281 matches in all competitions since his arrival in January 2018.
The former Southampton and Celtic man recalled how it was "easy" to get away from his marker Thomas Partey at his successful set-piece, although he also affirmed that there was a slice of luck involved.
Van Dijk: 'It was easy to get away from Partey'
"It's a very tough place to come, teams have noticed that over the years. They have created a solid team and make it difficult for everyone. To come back twice is a good thing, we take the point - that's the feeling," Van Dijk added.
"When I was marked by Thomas Partey, he only looked at me, so it was quite easy to get away from him. You need a bit of luck, and I was there to tap it in. I try to be important on every set piece we have.
"You play here, they create momentum, so you have to be ready to fight. That was the message. One point, we take it, we move now to the Carabao Cup."
Liverpool's draw in North London sees them remain second in the Premier League table, one point adrift of leaders Manchester City and four clear of the Gunners in third place.
Arne Slot's side now head to Brighton & Hove Albion on Wednesday evening for the EFL Cup fourth round before hosting the Seagulls in Premier League action on November 2.