Chris Boyd's side were 42-17 down with just 10 minutes to go, but they scored three tries late on to secure not only a losing bonus point but a try bonus point, too.
It was an incredible late show in a game that Saracens seemed to have taken away from the black, green and gold when they flew out of the blocks at the start of the second half.
Saints had led 10-9 at the break, despite being reduced to 13 men when Alex Coles and Lewis Ludlam were yellow carded.
But Saracens turned things around in impressive fashion, grabbing five tries as they continued to pile the pressure on.
Saints refused to be deterred though, knowing how vital it was that they took something from the game.
Replacements Rory Hutchinson and Tom James, who got two, scored before Matt Proctor delivered a fantastic finish from the final play of the game.
It meant Saints moved two points clear of Gloucester, who had taken a losing bonus point from their game at Harlequins earlier in the day, as the battle for fourth place continues into the final day.
Saints had headed to StoneX Stadium on the back of five successive bonus-point wins in the Premiership, but they had not played for more than three weeks.
Saracens, who had been eliminated from Europe seven days earlier, started faster and took a very early lead as Owen Farrell slotted a penalty.
Saints soon gave away another breakdown penalty but they made amends with huge defence from Courtney Lawes turning the ball over.
Saracens were being given plenty of chances to apply the pressure though as Saints struggled to get out of their own 22.
Farrell added a second penalty to the tally as his side pushed forward in relentless fashion.
Saints finally got a chance to do some attacking of their own, but after coming close to the home line they were driven back to close to halfway.
Coles was then yellow carded for not retreating, puncturing the away side's momentum.
Ludlam soon followed Coles off the field for an incredibly harsh decision that saw him punished for apparent contact with the head of Farrell while clearing out.
During the period that followed, Saints produced an incredible show of character, not only holding out but also putting pressure on at the other end of the field.
Dan Biggar gave the away side some reward for their huge efforts, slotting a penalty, won by Mike Haywood's jackal, six minutes before the break.
Saints weren't done there as Haywood again had a huge impact, producing a fantastic pass that allowed Tommy Freeman, who had run a superb line, to finish.
Biggar added the extras and Saints had a 10-6 lead with a minute to go before the break.
But Farrell still had time to cut the gap to a point, landing his third penalty of the first half.
And Saracens came out firing at the start of the second half, with Nick Tompkins twice breaking the Saints line before scoring.
Farrell converted and Saints were six points down again.
It soon got worse as Rotimi Segun ripped the away side apart and after George Furbank wasn't rewarded for a good tackle close to his own line, Alex Lewington walked it in out wide.
Farrell converted and Saracens were now flying, with Saints well and truly up against it in a game that had completely turned in the space of six second-half minutes.
Saracens didn't have to wait long for another score as Theo McFarland charged down Alex Mitchell's attempted clearance before juggling with the ball and grounding it.
Farrell missed the conversion but his side were now 28-10 up and Saints had so much work to do to get back in the game.
But they started to scale the mountain when Furbank charged forward and offloaded to Hutchinson, who scored with his first touch.
Biggar converted but Saracens soon hit Saints with a sucker punch as McFarland intercepted inside his own half and showed incredible speed before finishing acrobatically in the corner.
Farrell converted, with some assistance from the post, and the game had gone well beyond Saints.
Alex Goode grabbed try No.5 for the hosts, weaving his way through after latching on to a clever kick ahead.
Farrell once again added the extras and it was looking like a really horrible second half for Saints.
But there was to be late joy as Freeman again lit things up with a fine run and offload for the onrushing James to score.
Biggar converted and Saints had eight minutes to grab a precious bonus-point try.
They did just that when James scored his second, and there was still time for Saints to salvage a second bonus point, this time of the losing variety, as Proctor produced a sensational finish in the corner.
Saracens: Goode (Taylor 72); Lewington (Lozowski 51), Daly, Tompkins, Segun; Farrell, Davies (van Zyl 64); M Vunipola (Adams-Hale 64), George (Lewis 72), Koch (Clarey 51); Itoje, Isiekwe; McFarland (Wray 60), Earl, B Vunipola (Hunter-Hill 72).
Saints: Furbank; Freeman, Proctor, Dingwall (Francis 69), Skosan (Hutchinson 56); Biggar, Mitchell (James 64); Iyogun (Waller 53), Haywood (Matavesi 47), Painter (Hill 45); Coles, Ratuniyarawa (Nansen 64); Lawes (Moon 69), Hinkley, Ludlam (c).
Referee: Matthew Carley