South African Brits did the damage in the middle with good support from lock Mouritz Botha as Goode stepped up a gear to cruise through between the posts as Jackson's kick helped them to a 7-3 lead.
Flanker Jacques Burger had already been sent to the sin bin for hauling down Saints number eight Roger Wilson and the side were wobbling as they conceded six penalties inside the first 20 minutes.
They were almost made to pay when Hugh Vyvyan got within a few feet of the line and it was only a sharp intervention from Myler to stop the onslaught as he mopped up to clear brilliantly.
In this enthralling topsy-turvy game, the momentum moved back towards Northampton as Tongan Tonga'uiha charged down the left and nothing was going to stop his large frame as he fell over the line to give his side a valuable one-point lead at the break.
The drama continued as the visitors struck back to reclaim the lead four minutes into the second period as great hands from Vyvyan set up Wyles who flew down the left wing to score his fifth try of the season.
As the pressure intensified in the final 10 minutes Myler drew the scores level with a crucial kick.
The noise grew even louder a few minutes later as the pack fell over the line for South African tighthead Mujati to pick up five critical points.
Back came Saracens and this time it was the decisive blow.
The video referee was required to confirm the score by Brits after another drive brought the score to 19-19, leaving Jackson to collect his thoughts and calmly slot over to send Saracens to Twickenham on 29 May.
Northampton director of rugby Jim Mallinder told BBC Radio Northampton: "Naturally, I'm very disappointed to come so close, to get ahead in the game in the second half and then to lose the game at the death.
"It's gone and we've got to reflect on a good season. We didn't keep our discipline as much as we should, that damaged us.
"For us to finish second in the Premiership, we'll take satisfaction from that. We've got some good players arriving over the summer, we're still getting stronger and next season we'll be fighting on all fronts again."
Saracens director of rugby Brendan Venter: "The margins between winning and losing are so small, and there is no doubt we could have lost that game.
"We knew that we had to stop Northampton behind the gain-line, and the guys tackled their hearts out - they have unbelievable character.
"I thought we just played some great rugby out there."
Northampton: Foden, Ashton, Clarke, Downey, Reihana, Myler, Dickson, Tonga'uiha, Hartley, Mujati, Fernandez Lobbe, Kruger, Dowson, Best, Wilson. Replacements: Ansbro for Reihana (43), Sharman for Hartley (73), Morris for Mujati (72), Lawes for Fernandez Lobbe (55).
Not Used: Dreyer, Easter, Dickens, Geraghty.
Saracens: Goode, Tagicakibau, Powell, Barritt, Wyles, Jackson, De Kock, Aguero, Brits, Du Plessis, Vyvyan, Botha, Burger, Saull, Joubert. Replacements: Hougaard for Goode (72), Ratuvou for Powell (47), Marshall for de Kock (72), Gill for Aguero (62), Skuse for Du Plessis (73), Ryder for Botha (68), Melck for Saull (68).
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