Their task was made easier when Ernesto Jiminez was given a straight red card nine minutes from half-time with Osael Romero's penalty putting El Salvador ahead.
However, the 10-man hosts drew level through Erick Ozuna eight minutes after the break but Ruben Israel's side prevailed with Lester Blanco scoring what proved to be the winner in the 66th minute.
The result sees El Salvador seemingly heading into the third round of qualifying where in all likelihood they will meet Mexico and Costa Rica as they bid to make their third World Cup finals and first since 1982.
The Dominican Republic have just one point from three games.
All Jackson's goals came in the first half with Olivier Occean also scoring before half-time.
Occean got a second seven minutes before the break before Iain Hume struck in the 73rd and 86th minutes.
St Kitts and Nevis are four points adrift after a 1-1 draw in Puerto Rico.
The visitors were 2-0 up after 11 minutes thanks to Maurice (5) and Kim Jaggy (11).
There were no further goals in the first half but Reginal Goreux scored twice in seven minutes (57,64) to put the match beyond doubt.
Maurice got his second a minute later with a penalty, Kervens Belfort added another spot-kick (73) before Maurice completed his hat-trick eight minutes from time.
Guatemala kept up their 100% record in Group E as they beat St Vincent and the Grenadines 3-0.
Mario Rodriguez scored twice with Dwight Pessarossi also finding the net.
Panama lead Group C after a 5-0 win in Panama thanks to goals by Amir Waithe (two), Luis Tejada, Blas Perez and Ricardo Buitrago.
In the final game, Surinam moved to within two points of El Salvador as Giovanni Drenthe scored the only goal against the Cayman Islands.
Goalkeeper Miguel Pitta was sent off for the Cayman Islands with three minutes left.