Though Notts were travelling to face a side who play in the League above, the opposition played like a team devoid of confidence and one who had lost four matches on the spin going into the encounter.
If truth be told, City - touted strongly for promotion before the season got underway - proved to be one of the weaker sides the Magpies have faced this season, despite their possession of a galaxy of relatively big-names and a highly-rated manager in former Yeovil chief Gary Johnson.
Johnson's side played most of the second half with 10 men, after midfielder Cole Skuse was sent off in the 59th minute for two bookable offences, but that's to take nothing away from the Magpies - whose run of poor form seems to have now well and truly ended.
Gudjon Thordarson's men gave a strong, determined performance that was well worthy of the two-goal cushion it eventually heralded. In fact, it could have been more.
But even McLaren must have been shocked in terms of how the Magpies' two efforts came about this afternoon.
Debutant Tann - a man with 8 career goals from 149 appearences going into the game - was the player to set the ball rolling, slotting home right on the brink of half-time to the delight and surprise of the travelling support.
And that same group of supporters were cheering even more intently when they saw a quite magnificent strike from captain Julien Baudet seal the victory in the 65th minute.
All this seemed a world away when a fairly makeshift-looking Notts County took to the field in-front of a clearly disgruntled home support. Matthew Gill returned to the starting line-up for the first time in over a month, in-place of the cup-tied Emmet Friars, with Mike Edwards dropping back into the back 3.
Meanwhile, Tann was preferred to Brian O'Callaghan as the replacement for the suspended Kelvin Wilson.
The start to the game told nothing of the tale that was about to unfold. City began well, with Notts unable to provide any form of service to front pairing Steve Scoffham and on-form Glynn Hurst.
The Robins really should have taken the lead in the fourth minute, but former Notts loanee James Quinn somehow fired over from short-range after the lively Steve Brooker's knock-down.
The introduction of targetman White seemed to coincide with the Magpies weathering the early storm, with the away side starting to apply some pressure of their own.
Pot-shots from Stacy Long and Mike Edwards had already occured, before Long fired in the best effort of the game so far, a blistering 25-yard volley that was well tipped-over by Steve Phillips. From the resulting corner, White was denied only by a goal-line clearence from Luke Wilkshire.
The home side were now playing nervously, with the home support growing restless at the lack of goal-mouth action. However, a rush of blood to the head of Kevin Pilkington nearly gifted them the lead in the 23rd minute.
The often-reliable Notts keeper charged off his line needlessly and was rounded by Quinn, whose square-ball looked certain to find his strike partner, before Tann intervened superbly with a sliding challenge.
The Magpies had otherwise looked pretty comfortable against their out-of-touch hosts, with the locals' agitation reminiscent of many home games at Meadow Lane during the previous campaign.
It was with practically the last kick of the first half that Thordarson's team were able to take the lead, much to the delight of the noisy 299 travelling supporters.
Lewis McMahon floated in a left-footed cross that deceived the City defence and bounced at the feet of Tann, who confidently swept the ball home from 12 yards.
Half Time: Bristol City 0-1 Notts County
Thordarson made his second enforced change at the break, with McMahon - who later appeared, worryingly, on crutches - coming off to be replaced by the more defensively-minded O'Callaghan.
Much as in the first period, the home side began intently - littering Pilkington's goal with long-range efforts - before fading as the half wore on.
Former Middlesborough midfielder Wilkshire had the best of the chances, but sliced high and wide when just 12 yards out, much to the disappointment of the increasingly restless Johnson.
City's pressure had well and truly disintegrated by the time Skuse was given his marching orders in the 59th minute for his second late challenge of the afternoon.
City were still playing with some intent though, with long-range shots from Bradley Orr and Wilkshire flashing wide, but the home side were to see any hope of a Bonfire Night comeback extinguished in the 66th minute courtesy of a Baudet rocket.
The Frenchman waved away Long and Rob Ullathorne - who'd both clearly intended on floating the ball in - and simply unleashed a strike that flew past Phillips and into the net via the underside of the crossbar.
It was a magnificent strike, capable of winning any game, and it was followed by delirious celebrations in-front of the travelling support.
After that wonderful effort, it was obvious to everyone in the ground that City had given up any hope of progressing to the Second Round, with the Magpies more-than comfortable in the final 25 minutes.
Pilkington was only really called-upon once, to save well from substitute Steven Gillespie, whilst Notts even pressed for a third goal - with Hurst only denied by a linesman's offside flag.
The closing stages saw the game turn increasingly nasty - with it being a near-miracle that no players followed Skuse down the tunnel. Not that the travelling support cared of course, the last time they travelled to Ashton Gate they saw their side thumped 5-0 by a team who looked destined for the Championship.
How things change.
Full Time: Bristol City 0-2 Notts County
An excellent away-day showing from Notts, who have now hopefully turned the corner after their almighty slide down the League Two table.
Since the change to a 3-5-2 formation, we've seen three vastly-improved performances, with yesterday's being the pick of the bunch.
Whilst the home supporters booed their own team off at the finish, many applauded the Magpies down the tunnel, a well-deserved gesture for the Notts players, who progress past the FA Cup First Round once again.
Match Ratings and Reaction to follow.