Both of Hendy's scores started from inside his own half as he showed incredible speed to put the home side to the sword.
The England Under-20s full-back also helped to set up a try for Piers Francis during a frantic second half, in which the five-pointers flowed.
Saints had gone in 14-13 down at half-time, despite scores from James Grayson and the lively Tom James.
But an already entertaining game stepped up a notch after the break as the two teams traded blows in enthralling fashion.
Eventually Saints put the game to bed as Frankie Sleightholme scored on his debut with two minutes to go, earning the black, green and gold their first Premiership Rugby Cup win of the season.
Saints had taken early control at StoneX Stadium as some patient play resulted in James producing a nice piece of setup play to deliver a score for Grayson, who finished well.
Grayson missed the conversion in windy conditions and Saints were soon forced into an early change, introducing George Patten for his debut in place of the injured Ollie Newman.
Saracens were soon level as Rotimi Segun latched on to a tidy grubber kick and dotted down with ease in the corner.
Manu Vunipola slotted the conversion well from out wide and Saracens had the lead.
Saints still showed their ability to threaten on the counter and after James and new signing Joel Matavesi helped to engineer a break, Saracens had to scramble well to win a penalty.
But Saints soon won a penalty of their own at the scrum, allowing Grayson to notch three points with a well-struck effort.
Saints were bossing the scrum battle, winning a second set-piece penalty soon after as they looked to build a lead.
But the attacking lineout went astray and Saracens were soon on the attack, earning a penalty that provided the platform for Kapeli Pifeleti to power over.
Vunipola again converted well and Saracens were starting to get in the ascendancy.
But Saints would have the final say before the break as the pack did the business with a lineout drive and James picked up and found a gap to score.
Grayson missed the conversion to leave his side a point down at the break.
Saints changed both of their props at half-time, with Nick Auterac and Karl Garside able to head off happy in the knowledge that they had both enjoyed a strong first 40 minutes.
That meant Danny Hobbs-Awoyemi came on for his first Saints appearance since September 2020 and Ed Prowse was introduced for his debut.
Saints made a strong start to the second half, with a couple of moments of magic from Tommy Freeman putting Saracens under pressure.
And the hosts soon cracked as Freeman forced his way over.
Grayson missed the conversion but Saints held an 18-14 lead, and they were pushing on in pursuit of their bonus-point try.
Josh Gillespie was just beaten to the ball after chipping it over the head of Segun, but Saints would get their fourth try soon after.
Segun kept the ball in play but only succeeded in batting it into the hands of Hendy, who gathered inside his own half and sprinted away to score behind the posts.
It was Hendy's third try in as many Premiership Rugby Cup games this season, and Grayson gleefully added the extras to make it 25-14.
Saracens hit back almost immediately as Brandon Jackson scored just after coming off the bench.
Vunipola's successful conversion meant the gap was back to four points again, with 17 minutes remaining.
Saints were seemingly still in control of the game, but they were hit by a sucker punch as Segun picked up a fine offload inside his own half and delivered an electric run and finish.
Vuinipola converted, but Saints hit back almost immediately in what was turning into a wild game.
Geordie Irvine played a key role before good work from Hendy and Grayson set up Francis, who finished well in the corner.
Grayson converted well from the touchline and Saints scored again almost immediately as Hendy gathered the kick-off and delivered a moment to remember, running in from inside his own half as he produced a special score.
Grayson again converted and Saints finally had some breathing space with 10 minutes to go.
But that didn't last long as Saracens kicked a penalty to the corner, and Ethan Lewis powered over.
Vunipola continued his fine kicking display with the conversion and, once again, the gap was four points.
But Sleightholme delivered the killer blow, scoring in the corner after another nice Saints move.
And Grayson's conversion put the gloss on a fine away win for the black, green and gold.
Saracens: Obatoyinbo (Moore 74); Harris, Hallett, Morris (Jackson 60), Segun; Vunipola, de Haas (Bryan 71); Mawi (Crean 40), Pifeleti (Lewis 40), Wainwright (Jeffries 51); McFarland, Hunter-Hill; Stonham, Wray (c) (Dan 56), Christie.
Saints: Freeman (Hendy 56); Gillespie, Francis (c), Matavesi (Sleightholme 72), Tuala; Grayson, James (Tupai 56); Auterac (Hobbs-Awoyemi 40), Fish (Haywood 34), Garside (Prowse 40); Moon, Frost; Tonks, Newman (Patten 5), Irvine.
Referee: Mike Hudson