Debutant Lindfield netted after 23 minutes before Dudfield added a late second on 88 minutes.
Charlie McParland made two changes to the side that got him his first win as Notts boss against Wrexham last week with both enforced.
Two of the best performers in that game were unavailable for selection with Matt Somner suspended and Spencer Weir-Daley taken ill yesterday.
That meant a debut for new loan signing Liverpool man Lindfield up front to partner Lawrie Dudfield and Gary Silk played the midfield holding role alongside Neil MacKenzie.
Andy Parkinson also missed out from the sixteen after failing a late fitness test.
A scrappy start between tenth placed Stanley and eighteenth positioned Notts County didn't come to any sort of life until the ninth minute when a half-chance fell to home midfielder James Harris but his hopeful long-range effort was over Kevin Pilkington's bar.
Notts hit back with their own half chance which fell to five-goal top scorer Richard Butcher who dragged a shot on his left foot only narrowly wide after being teed up by Lindfield.
Wide man Myles Weston was starting to get into the game for Notts and causing Stanley captain Peter Cavanagh no end of problems in what was NCM's key battle of the day, but the final product had been lacking in the first twenty minutes.
Then it was new boy Lindfield who got into the game in the most impressive of fashions, netting a debut goal to give Notts a 23rd minute lead after Dudfield had worked hard to force the Stanley defence into confusion before laying in the Liverpool youngster who cleverly finished.
McParland had brought the nineteen year old to the club charged specifically with taking the chances the Magpies strikers had largely failed to do so far this term - and what a superb start.
They nearly gifted Stanley an immediate equaliser however when an Adam Tann slip when caught from position but in-form Stanley striker Roscoe D'Sane failed to capitalise thanks to a good save from Pilkington.
Stanley were growing in the game, particularly with Weston starting to find himself on the periphery of the action, and Mark Roberts powerfully headed wide from a corner, before another long range Harris strike was blocked by Stephen Hunt.
The Notts captain was again alert to danger when he superbly denied D'Sane a shot on goal with a last ditch tackle.
Finally Notts started to play again and on the 43rd minute it was strike duo Dudfield and Lindfield again who worked well together and as the ball fell invitingly to Lindfield he hit it well and only narrowly missed the target with home keeper Ian Dunbavin well beaten.
One more chance came before the break and it fell to Stanley midfielder Ian Craney after a fourth Stanley corner, but his finishing effort from the edge of the box whistled wide.
After two added minutes the referee blew for half-time - the first time this season that Notts had led an away game at the break.
Neither McParland or home boss John Coleman made any changes at the break as the attendance was announced at just 1,722.
Paul Mayo was the first to see a yellow card in the game for kicking the ball away as Notts immediately resolved to the tactic of seeing the game out as best as possible.
Stanley were pushing hard and several times their crowd rose in anticipation but Tann and in particular Hunt seemed to be there to clear the danger on most occasions.
Lindfield rose with Dunbavin after a good Weston cross but Dunbavin closed the ball well, before Lindfield laid MacKenzie on only for last week's man of the match to slice wide.
D'Sane, forever the danger man, soon called Pilkington into action once more but the Notts keeper remained on top of that particular battle by producing good low save after D'Sane's shot was powerfully hit from the edge of the box. After initially spilling the ball Pilkington did well to gather it.
The ante was being upped by the hosts but Notts remained largely resolute and forced Craney into a long-range effort when other options were open to him - as it turned out the 59th minute drive very nearly dipped in but it seemed to be always going off target.
The pacey D'Sane resumed his battle with Pilkington once more after neatly turning Hunt but again the Notts keeper was more than equal to it.
After Dudfield joined Mayo in the book for the same offence, Notts had a slight shout for a penalty after a long-range Mayo effort was pushed out by Dunbavin towards the onrushing and ever alert Dudfield who seemed poised to score but was pulled back by desperate Stanley defenders.
After 76 minutes Hector Sam was introduced by McParland for goalscorer Lindfield who deservedly left the field to a standing ovation from the Notts fans who were hopeful his debut strike would bring Notts their first away win of the campaign.
With ten minutes remaining Notts hearts were in their mouths as Shaun Whalley hits an angled drive from eighteen yards but it whistles just wide.
The first Stanley change saw former Macclesfield man John Miles - a scorer past Notts in the past - introduced for Whalley.
With five left on the clock the best chance of the game fell to the previously quiet home top scorer Paul Mullin after a low cross but a yard out he can only stab against the post, only to see the linesman flagging for offside in any case.
Austin McCann was introduced to shore things up for the hardworking Weston for Notts, but immediately after the game was sealed and deservedly so for the hard working Dudfield - who so badly needed a goal to add to his all-round impressive performance.
It came in the 88th minute, as Sam won a corner after his shot was
The first away win of the season - and first since last Easter at Wrexham - had deservedly come for McParland's men, with the clean sheet an added bonus.
But all the talk was sure to be of new man Lindfield and strike partner Dudfield - did you hear that former strike hero Tommy Johnson is back at the club? Coincidence?