In front of over 4,200 fans, it was Robby Sandrock who scored twice on the powerplay to lead the Belfast side to victory.
It was visiting Hull who drew first blood though, with Kurtis Dulle netting after just 50 seconds.
The Giants battled back to draw level just after 10 minutes, courtesy of Kevin Saurette, and Greg Stewart adding a second gave the hosts an important 2-1 lead going into the first break.
The second period started with more promise for the Giants - Colin Shields netted to make it 3-1.
It was Dulle who replied for the Stingrays though, with his second of the night.
Sandrock blasted his first goal into the top corner of the net though and a second followed in the third period.
Tom Squires managed what would be the Stingrays final goal 13 minutes into the third but, although the Stingrays fought hard, Garrett Zemlak in nets and the Giants defence shut down the game.
The Belfast side take the 5-4 win into their second game of the weekend, as they travel to Wales to meet the Cardiff Devils on Sunday.