The 31-year-old midfielder's first-half effort was enough to clinch a Wembley date against the Capital One Cup runners-up, with the hosts missing a penalty moments before
Despite holding a 1-0 advantage from the first leg at Sixfields Stadium, Aidy Boothroyd’s side boasted the second-worst away form in the league against a team who were unbeaten at home since January.
But the Cobblers started the strongest, with first-leg goalscorer Roy O'Donovan going close after Adebayo Akinfenwa’s fine through-ball in the only highlight of a scrappy opening period.
The game was brought to life after 15 minutes when Ben Tozer hauled down Cheltenham striker Russell Penn outside the penalty area, only for the referee to point to the spot.
Marlon Pack stepped up but was thwarted by a fine save from Lee Nicholls, flinging himself low down to his right-hand side to preserve his side’s slim aggregate lead.
The missed penalty only served to reinvigorate the away side, and they soon took the lead in headline-grabbing fashion when Guttridge latched on to Akinfenwa’s knock down to hit a sensational half-volley past Scott Brown from distance.
Cheltenham looked dejected, seeing a two-goal deficit to overturn, and started the second half in similar sluggish fashion - with striker Darryl Duffy in particular failing to make an impact on the game.
Top goalscorer Shaun Harrad was soon thrown into the fray just past the hour mark and his introduction sparked a new lease of life for the hosts.
With 15 minutes left to play, Cheltenham created their two best chances of the game when substitute Kaid Mohamed thundered a point-blank shot off the crossbar following a brilliant cross by Sido Jombati, with Nicholls beaten all ends up.
And, two minutes later, the Robins again went close with Sam Deering stinging Nicholls' palms with a rasping drive from inside the penalty area.
Cheltenham continued to battle, with Nicholls again matching their opponents' best - pushing away Harrad's late effort on the angle in the dying moments - but it was Northampton who were celebrating at full-time and will now face Bradford in the Leaguue Two play-off final at Wembley on May 18