Alexandre Lacazette also netted at the other end but teammate Shkodran Mustafi was clearly in an offside position.
His challenge on van Dijk might have resulted in either a goal or a penalty for Liverpool and the attempt to catch Mane's centre while at full stretch could have been a game-settling howler.
They created more chances with Arsenal having 12 and Liverpool 13, but putting it on frame was a struggle for both.
Salah smashed an incredible 32 goals in 36 Premier League games in 2017-18 in his first campaign since moving from Roma.
The Gunners, however, had the goal they deserved to celebrated eight minutes from time when Lacazette found space behind Liverpool's defensive line, evaded an out coming Alisson and curled the ball exquisitely into the far corner.
The England global will have a long and successful career at Anfield, something that fans have known since he fully broke into the first team last season and showed some mature performances against top opposition.More news: Indonesia Lion Air flight crashes with 189 aboard
"We wanted to win but the performance is good, we push and we work the match, doing our tactics and with our supporters pushing us with energy", he said.
After somewhat stagnating under the guidance of legendary manager Arsene Wenger in recent seasons, Arsenal have bombarded their way back into contention at the top of the Premier League table.
The full-back struggled to cope with Arsenal's attacking threat down the left-hand channel and Gillespie admits it was one of the worst displays he has seen from the youngster.
Liverpool looked on course for three points at the Emirates Stadium when James Milner gave Liverpool the lead shortly after the hour mark.
They'd have ranked 17th in the Premier League if the full-time whistle came after 45 minutes in the Premier League this season, while Liverpool had the best record at the break, going into this weekend. They play the ball through and could score the goal. Arsenal kept at it and got a point.
And during a post-game interview, Milner was asked what taking five points from games against City, Chelsea, the Gunners and Tottenham says about the progress made under Klopp - and his reply was a characteristically Yorkshireman one.
While his pace and hints of trickery went down well, Iwobi was generally considered to be erratic and unimpressive with his final pass.