In pouring rain, Osei Telesford scored on a deflected shot in 15th minute and Noah Delgado and Edwin Miranda struck in the 38th and 50th, respectively, before Christian Benitez scored Santos' consolation goal in the 71st.
The Islanders were playing two days after winning the regular season title in the USL First Division.
Telesford scored on a header, connecting with goalkeeper Miguel Becerra's rebound of Petter Villegas' shot.
Delgado struck home by redirecting Jonathan Steele's shot from outside the penalty area.
Miranda scored on a 25-yard, right-footed drive that skipped inside the left post.
The Islanders and fellow USL club Montreal have remained unbeaten in seven Champions League matches. Each won and tied in the preliminary round and won their group openers last week.
In the Preliminary Round, the Islanders eliminated two-time Concacaf champion Alajuelense of Costa Rica on 3-2 aggregate.
The Islanders beat Panama's Tauro FC, 2-1, in their Group D opener.
Montreal, which faces Mexico's Atlante on Wednesday, beat Trinidad's Joe Public, 2-0, in its Group C opener.
In Group A action on Tuesday, Mexico's Cruz Azul thumped Costa Rica's Saprissa, 4-0.