Two individual moments of brilliance in 14 first-half minutes settled the game. First goalkeeper Lee Nicholls kept the Cobblers' 1-0 lead from Thursday's first leg intact with a fine save to keep out Marlon Pack's 14th-minute penalty, before a long-range thunderbolt from Guttridge put them in control.
And despite Cheltenham's best efforts, they never really threatened a memorable comeback until Kaid Mohamed's header crashed off the crossbar with 14 minutes remaining as the visitors registered a 2-0 aggregate victory and with it, moved a step closer to a return to the third tier after four seasons.
The Robins have struggled for goals in recent weeks and have failed to net since Russell Penn's strike in their 1-0 win over Exeter on April 20. But a foul by Ben Tozer on the midfielder right on the edge of the box handed them the perfect chance to end that run in the 13th minute.
After the controversy over the decision to point to the spot died down, Pack's fourth penalty of the campaign was saved superbly by Nicholls. The Wigan loanee plunged low to his left-hand side to spark wild celebrations amongst the travelling fans behind his goal.
In the 28th minute and with their first real effort of note, Guttridge moved his side a step closer to Wembley with a goal fit to grace his country's national stadium. Latching on to Adebayo Akinfenwa's knock-down the midfielder let the ball bounce before smashing home an unstoppable volley from 25 yards. The 31-year-old's second of the season was the first Scott Brown had conceded at home since March 2.
With 18 minutes to go Brown kept the Robins in the tie as he denied Chris Hackett when the former Millwall man was sent one-on-one with the stopper.
The home side were then inches away from clawing their way back into the tie when substitute Mohamed's header rattled the woodwork.
And while the final whistle sparked jubilant scenes amongst those in green with a May 18 Wembley date now on the horizon, Cheltenham were left to reflect on play-off heartache for the second successive season.