Marc Richards, Eoin Doyle, Jimmy Ryan, Gary McSheffrey and Tendayi Darikwa all slotted their spot kicks away, with Ollie Banks the only player to miss.
Talbot blasted the winning penalty past Oldham goalkeeper Paul Rachubka to seal a memorable night for the North Derbyshire side.
In regular time, Danny Philliskirk had opened the scoring for the Latics in the opening 20 minutes; however the Spireites found an equaliser through Darikwa just eight minutes later.
After a frantic last couple minutes where the Spireites endured intense pressure, they eventually held out and they now face Fleetwood Town in the Johnstone's Paint Trophy area finals.
Chesterfield made four changes to the side that bowed out of the FA Cup on Saturday as Richards led the line for the first time since the draw with Scunthorpe last month.
The game started at a frantic pace and within the first minute of the game, a short pass in the midfield presented Banks with an opportunity to have an early run at the defence. The midfielder unleashed a strike from the edge of the area which only just whisked past Rachubka's post.
Oldham turned defence into attack only a minute later as Michael Petrasso was presented with a strike on goal but the ball smashed the side netting to the relief of Lee.
Petrasso was receiving a lot of space out wide in the opening ten minutes but the Spireites looked dangerous on the counter attack; proven when Darikwa broke free on the right, but was unfortunate to not find a blue shirt in the box.
It was Oldham that took the early advantage as they took the lead on 20 minutes. Philliskirk found space in the area and tucked it past Lee with the goalkeeper helpless.
As tempers started to rise, Ritchie Humphreys was the first player to receive a yellow card after a hard tackle on Petrasso was punished by the referee.
Chesterfield nearly responded in perfect fashion through a superb team move. Doyle played the ball wide for Darikwa who smashed a volley just wide of the Oldham goal.
That was a warning sign for the Latics as it was the winger who levelled the tie just before the half hour. Doyle played another ball out wide towards Drew Talbot who delivered a delightful cross onto the head of Darikwa and the ball looped over Rachubka and into the far post.
A couple of minutes after the goal came a huge talking point in the game as it appeared Ian Evatt had brought down Oldham winger David Mellor in the area and to everyone’s surprise the referee awarded a goal kick instead of a spot kick.
That decision seemed to spur the Spireites on and goalscorer, Darikwa had a superb opportunity to put the Spireites ahead with five minutes to go until half time. The winger created space, knocked the ball past the last defender but as he raced through, he fired the wrong side of the post.
Chesterfield ended the half strongly, causing a succession of corners with Liam Cooper going very close from Ryan’s delivery.
Both sides struggled to gain the upper hand as the second half restarted. Oldham came closest in the first five minutes of the half as Philliskirk tested Lee’s palms but the goalkeeper pulled off a great save at his far post to keep the scores level.
Distressing signs followed as Ryan looked to have seriously injured his shoulder however the midfielder valiantly picked himself up and soldiered on.
Sam Hird was the second Chestersfield player to enter the referee’s notebook as he was booked for a foul on an Oldham defender. Jonson Clarke-Harris struck the free kick from 30 yards which Lee did well to save at his near post.
With just over ten minutes of the game remaining, Oldham had their best chance to win the game in normal time. Former Spireite loanee, Jonathan Grounds danced past the defence and unleashed a shot which Lee again did really well to keep out and the danger was cleared.
Talbot was the third player to go into the book for the Spireites as he cynically brought down an Oldham attacker as they looked to break.
With only five minutes of the game remaining, Chesterfield were more than matching their League 1 opponents but were coming under increased pressure.
Substitute, Adam Rooney turned Cooper and raced clear in the dying embers of the game however the former Spireites striker hit his effort straight at Lee.
McSheffrey was introduced deep into injury time as he replaced the injured Cooper.
The home side had a penalty turned away in the final minute of added on time and the game eventually would be decided by a penalty shootout.
With the scores at five apiece, Anton Rodgers’ penalty was expertly saved by Lee and that presented Drew Talbot with the opportunity to win it. He stepped up and smashed the winning spot kick to send the Spireites into the final of the Northern Area Final.
Oldham Athletic: Rachubka, Grounds, Wesolowski (Rodgers 86'), Kusunga, Tarkowski, Smith (c), Mellor, Clarke-Harris, Lanzoni, Petrasso (Rooney 81'), Phillishark.
Subs not used: Oxley, Winchester, Plummer.
Chesterfield: Lee; Talbot, Evatt (c), Cooper (McSheffrey 90+2), Humphreys; Ryan, Hird, Darikwa, Banks, Doyle; Richards.
Subs not used: Chapman, Togwell, Devitt, Gnanduillet.