The Jamaicans finished atop Group D with six points, three better than the Dominican Republic.
Broderick scored in the 46th and 75th minutes Sunday, and Shantel Bailey added another in the 90th, to pace Jamaica. Broderick scored the final two goals in a 9-0 rout over Aruba on Thursday, when Bailey also had a goal. Shantell Thompson and Shadie Shirley had three each in the Aruba victory.
The Dominican Republic beat Aruba 7-0, led by Anajaira Claudio's two goals, on Friday, meaning Jamaica needed only a draw on Sunday to advance.
Jamaica joins the Bahamas and Guyana in the second round of qualifying along with the winner of Group B, which will be played on a home-and-away basis between Dominica, Trinidad & Tobago and St. Kitts and Nevis beginning September 13. The final game is set for October 4.
Three teams from the second round will advance to the CONCACAF finals.