Steve Owre scored for his third consecutive game and Scott Conway grabbed his team-leading 39th goal of the season to help Adam Keefe's side into a share of top spot in the Elite League alongside the Guildford Flames.
The Giants were the first team tested on the penalty kill as Ben Lake was called for hooking, but an aggressive special teams effort saw the Panthers kept off the scoresheet on the powerplay.
The rest of the period proved to be a battle of the netminders, and while Beskorowany had to be huge to deny new Panthers signing Niko Lahtinen as he tried to jam the puck home on the doorstep, it was Peyton Jones who was far the busier at the other end.
The former Giants goaltender first made a superb double save to deny David Gilbert and Ciaran Long, then he had to react quickly to prevent Scott Conway from putting a puck in from behind the net after Sean Norris and Will Cullen had big chances.
But his best save came right at the end of the first period, a giveaway from Nottingham in their own zone allowing Gilbert in on goal for the shot but Jones stretched out a pad to deny him at the last second.
The goaltender battle continued in the middle frame and Beskorowany came up with his best save of the game when David Levin drove to the net and fired a backhand towards the top corner but was denied.
Unfortunately for the Giants, Jones was equally as good at the other end as he once again prevented Conway from opening the scoring with an excellent pad save on a one-timer before blanking Mark Cooper's one-on-one effort.
The Giants survived an early scare in the third period when Jeremy Welsh fired a rebound on goal that came back off the bar, with the officials needing a video review to determine it hadn't actually come back out off the back bar.
But after the correct decision was made, it was the Giants who pulled ahead instead, captain David Goodwin firing the puck back in front for Owre who rifled it home from the slot at 50:27 for the game-winning goal. (0-1)
Searching for the tying goal, the Panthers pulled Jones for the extra skater, but it proved to work in the Giants' favour as Conway picked up on the loose puck in his own zone and fired it the length of the ice for the clinching goal at 59:33. (0-2)
The Stena Line Belfast Giants remain on the road as they face the Guildford Flames on Wednesday 15 February, before returning to The SSE Arena, Belfast on Saturday 18 February to take on Glasgow Clan. Tickets are on sale HERE!