The runners-up in Sweden and the fourth-placed side in Belgium last season both began their European campaigns at 3Arena, and it was a campaign that began brightly for Anderlecht, who took the lead just six minutes in.
The visitors won themselves a free-kick 25 yards from goal, and Danylo Sikan needed no second invitation to power it into the top corner with his right foot, giving Warner Hahn no chance.
Hammarby almost made the perfect response a minute later, but Colin Coosemans was equal to a well-struck free-kick from Victor Eriksson. Markus Karlsson and Nahir Besara also had chances for Bajen, before Hahn kept his side in the match with a fine save from Ali Maamar in the final 10 minutes of the half.
Karlsson continued to look dangerous in the second half for the hosts, who were given a lifeline 11 minutes from time when Nathan Saliba - fresh from representing Canada at the World Cup - was shown a second yellow card.
Three minutes from time, Hammarby threw on Frank Adjei in an attempt to break the 10 men down, and it took all of two minutes to pay dividends, as he was in the right place to bundle home a rebound inside the area.
There was a nervous wait inside the ground before a VAR review finally confirmed the goal would stand, ensuring Hammarby will travel to Brussels on level terms ahead of the second leg on 30th July.