The Grecians could and should have got something out of the contest and had Lee Elam not squandered a gilt-edged chance moments before Soares' opener, it might have been a different story.
Sadly this has been the tale of the season - so near and yet so far - as City suffered only the second defeat of the campaign.
It leaves Paul Tisdale's men 13 points adrift of Blue Square Premier leaders Torquay United and with only one win from their last nine games.
Tisdale made his players aware of the club's Recreation Ground hoodoo ahead of the game in an effort to fire them up.
And while they were more than a match for their high-flying hosts, they failed to convert the chances that came their way and were left to count the cost.
An unwelcome tag as the draw specialists of the Blue Square Premier had attached itself to Exeter following seven stalemates from their opening 12 games heading into last night's encounter.
Tisdale, not afraid to switch personnel and formations this season, opted to keep faith with the side and the 4-5-1 system that carved out a point at the Kingfield Stadium last time out.
The only notable change was that Steve Basham had recovered sufficiently from a fractured rib to take his place on the bench at the expense of defender Matt Taylor, as the City boss named an essentially attacking bench. Aldershot boss Gary Waddock, whose side had already been beaten twice on home soil by Crawley Town and Torquay United, had ordered his side not to slip into the comfort zone to ensure they kept up the pressure at the top of the table.
And he warned that the Grecians posed a major obstacle for his newly assembled side, which preserved their unbeaten away record courtesy of a late equaliser at Cambridge United last weekend.
Waddock made just one change from that side with defender Dean Smith replacing Rob Gier at right back.
The game began at a lively pace with neither side able to stamp their authority on proceedings.
The Shots threatened to draw first blood when Anthony Straker launched an ambitious 25-yarder marginally past Andy Marriott's right-hand post and Jon Richardson's header was comfortably collected by Nikki Bull at the other end.
With the hosts buoyed by their passionate home supporters, Dave Winfield had a glorious chance to test Marriott on 12 minutes but saw the ball bobble off his thigh after Lewis Chalmers' long throw had landed invitingly at his feet.
Jamie Mackie, once again deployed in the loan striker role, was getting caught offside on too many occasions as the visitors looked to prise open an Aldershot rearguard that has now conceded 16 goals in their opening 13 games.
Although the Grecians enjoyed the bulk of the possession in the opening quarter, Ben Harding's thunderous left-footed drive took a deflection and whistled inches past Marriott's post.
Winfield was rapped for a late tackle on Bertie Cozic and that served to fire up the away side, who began to pile on the pressure.
Mackie's mazy run left Rob Elvins in a spin before forcing Bull into a comfortable save and Stansfield watched his attempted shot deflected out for a corner.
And when Moxey delivered a peach of a corner, Richardson arrived with precision timing to plant a header the wrong side of the upright.
City's recent inability to defend set-pieces almost came back to haunt them on 38 minutes when Rhys Day's header was destined for the top corner until skipper Matt Gill produced a crucial headed clearance on the goalline.
Aldershot, who have established a reputation as one of the most effective attacking forces in the Blue Square Premier, lacked any real imagination going forward, with the City defence coping comfortably with fleeting moments of danger.
George Friend rose to meet Matt Gill's free-kick at the beginning of the second half, only to see his rising header clear the crossbar.
A great run from Adam Stansfield left Day and Soares trailing in his wake before drilling over a cross for Lee Elam to stab wide. Moments later the visitors survived a scare when Scott Davies released Elvins and, after cutting inside, the striker steered his effort beyond Marriott's left-hand post.
Soares was then gifted oceans of space in the area, but his shot came back off the foot of the post and into the arms of a grateful Marriott.
Shots striker John Grant, a peripheral figure for the majority of the game, sent a header over the bar following Davies' teasing free-kick. Mackie had a chance, put through by Elam, but his weak shot that was easily collected by Bull.
Leading goalscorer Richard Logan was introduced in the 73rd minute in place of Bertie Cozic as Tisdale switched to a 4-4-2 formation.
The complexion of the game then changed dramatically in the space of 30 seconds.
First Elam skipped clear of the Aldershot defence but put his shot far too close to Bull, who pulled off a fine save.
Then the hosts swept up the other end with Soares unleashing a stinging effort that got a deflection off Dean Moxey to leave Marriott with no chance.
Joel Grant poured salt into the wounds on 82 minutes when he lashed an unstoppable shot beyond Marriott.
So the wait goes on for a win at the Recreation Ground and the wait goes on for Exeter City to get their season off and running.
Aldershot Town: Bull, Smith, Winfield, Day, Straker, Soares, Chalmers (Newman, 84), Davies (Jole Grant, 63), Harding, Grant, Elvins
Subs not used: Gier, Jaimez Ruiz, Hudson
Exeter City: Marriott, Tully, Friend, Edwards, Moxey, (Basham, 82), Gill, Richardson, Cozic, (Logan, 73), Stansfield, Elam, Mackie, (Carlisle, 82)
Subs not used: Jones, Artus
Source: http://www.thisisexeter.co.uk/