Captain Armand Anebo scored the go-ahead basket in the final 30 seconds in his first appearance of the season before the home side were able to seal the win from the free throw line.
D’Andre Bullard had a debut to remember for Leeds as he finished with 17 points, eight rebounds and five assists on debut with Louis Sayers also adding 17 points in the win.
Rob Marsden pulled down a mammoth 17 rebounds to go with his eight points before fouling out with more than five minutes remaining.
Tayo Ogedengbe led the visitors with a game-high 26 points and he got Surrey going with 11 points early on including three straight 3-pointers. Will Neighbour would give the visitors a 15-20 advantage at the end of the first after making 3/3 from the free throw line.
Leeds took the lead with the first six points of the second before the lead changed hands several times throughout the period. Bullard scored six points in an 8-0 run to help his new side into a 33-32 lead at the half-time interval.
The lead was pushed up to seven on a Sayers three when play resumed in the third, but the advantage was short-lived as Surrey quickly levelled before edging back ahead on a 14-4 run.
Sayers would then net back-to-back triples in the final minute to give Leeds a 54-51 advantage heading into the final quarter. Dwayne Camille extended the lead with another 3-pointer, but once again Surrey hit back to set up a tense finale as the lead swayed from one side to the other in the fourth.
Felder, who posted a double-double of 14 points and 10 rebounds from the bench, twice pushed the visitors ahead after Marsden fouled out, while Ogedengbe had given Surrey a slender 66-67 inside the final two minutes.
Camille scored six points in quick succession before Anebo put his side ahead with 25 seconds left and with Surrey unable to respond, Leeds were able to close the game out at the foul line to improve to a 2-3 record.