This was no kick and rush performance by the Midlands side. County rose to the occasion with a battling performance. Even after they took a lead midway through the first half, they refuse to adopt a closed shop policy.
No wonder the players and supporters were jubilant after the final whistle.
Former Chelsea defender Robert Huth made his first-team debut for Boro, who were captained by Australian Mark Viduka on his return to the side.
The visitors created the first scoring chance when Lawrie Dudfield broke through and shot just wide off the far post.
County took the lead in the 26th minute when they cashed in on a defensive blunder by Anthony McMahon.
Tcham N'Toya gave Ross Turnbull no chance with his shot and celebrated his goal with a somersault.
Stuart Parnaby shot wide for Middlesbrough and Lee Cattermole headed wide shortly afterwards, before Cattermole was booked for a foul.
Notts County were giving a spirited display, although it took a brilliant save from Saul Deeney to deny Viduka an equaliser.
Just before the break Viduka crashed a shot from eight yards into the sidenetting.
Gaizka Mendieta then wasted a scoring chance for Middlesbrough when he shot wide just after the break.
County covered well in defence to restrict the number of openings for the home side.
Boro certainly found the route to goal difficult, while at the other end Dudfield shot wide at the other end.
Boro then brought on former Charlton forward Jason Euell in a late bit to pull the game round.
N'Toya wasted a chance to seal the game for the visitors, before there was a terrific scramble in the Magpies area with the visitors clearing three goal attempts.
Middlesbrough understandably upped up the tempo in a bid to save the game.
Parnaby missed a chance to equalise when he shot over the bar and County were not happy when five minutes of added time was announced.
However, they survived some tense moments with Boro keeper Turnbull even joining the attack in a desperate bid to avoid a cup shock.