Salah put the Premier League champions ahead in the first minute, latching on to a poor backpass and bursting goalwards before slipping the ball past goalkeeper Jesper Hansen.
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Brazilian striker Antony opened the scoring inside the first minute with skipper Dusan Tadic netting the other as Ajax moved into second in the standings with four points after three games
Goals from Diogo Jota and a Mohamed Salah penalty kick secured victory for the 2018/2019 champions.
Midfielder Fabinho has been filling in for Van Dijk in the centre of defence since the Dutchman suffered a serious knee injury in the Merseyside derby against Everton.
The match was played in driving rain at the MCH Arena in Herning on Wednesday.