Real Madrid and Tottenham, which tied, 1-1, remain tied atop the group while APOEL and Borussia Dortmund have each managed only one point.
Borussia Dortmund started its 2017-18 Champions League campaign with 3-1 losses at Tottenham and at home to Real Madrid.
Pulisic, who started against APOEL after coming on as a halftime sub, upon returning from USA duty, in last weekend’s 3-2 loss to RB Leipzig, shot high in the 64th minute from outside the penalty area and set up a shot for Mario Goetze in the 71st minute that was blocked.
Mickael Pote had given APOEL the lead in the 62nd minute and Sokratis Papastathopoulos equalized in the 67th minute.
BVB, which managed only one shot in the first half, trails Tottenham and Real Madrid by six points in the group from which the top two advance and the third-place team moves to the Europa League.
In the Bundesliga, BVB is in first place, two points ahead of Bayern Munich and three points ahead of RB Leipzig.