The Eagles had lost two straight league games heading into the clash and made a fast start with a 15-6 opening. However, the Scorchers hit back with a strong response to take the lead at 18-19.
Jackman netted twice from downtown in an 8-0 run for the Eagles before an 11-2 start to the second saw the Scorchers build their largest lead of the game.
Newcastle re-gained control to go up by seven at the interval and pushed on in the third as they established a double-digit advantage heading into the final 10 minutes.
A 15-5 spell gave Surrey a glimmer of hope late on with Tayo Ogedengbe's basket cutting the gap to six with over a minute left.
The Eagles held firm and finished the game in style to keep up the pressure on league leaders, Leicester Riders, who were also victorious on the night.
Report from bbl.org.uk.