The financially-troubled League Two club were in dreamland heading into the break on the back of goals from striker Lee Hughes and Ben Davies.
Wigan spared their blushes in the second period as Jason Scotland and Watson hit back to force a February 2 replay at the DW Stadium.
For County, the tie was played against the backdrop of another High Court winding-up petition due to be heard on Wednesday.
Despite their off-field problems, the players' minds appeared focused as they produced a rousing opening 45 minutes to savour.
Remarkably, other than one change, this was the same Notts County team that had struggled to overcome non-league strugglers Forest Green Rovers in Tuesday's home third-round tie.
But cometh the hour, cometh the men, as Wigan found to their cost during a tortuous first half in which they barely roused themselves above the mundane.
Hughes served notice of his intent after just five minutes after taking a right-wing ball from Craig Westcarr in his stride.
However, he dragged his 15-yard shot across debutant goalkeeper Vladimir Stojkovic and a yard wide of the Serbian's right-hand post.
Stojkovic was one of six changes made by boss Roberto Martinez, with Chris Kirkland rested, captain Mario Melchiot and influential midfielder Paul Scharner injured, Hendry Thomas suspended and Gary Caldwell and Charles N'Zogbia benched.
But this was still a Wigan side, 62 places above their opponents in the league pyramid, that should not have been as embarrassed as the Latics were in the first half.
One of the few bright spots during the opening period, aside from their fluorescent orange shirts, came in the 24th minute when Hugo Rodallega saw a 20-yard drive touched onto the right-hand post by Kaspar Schmeichel.
Schmeichel's fortune held when, with no Wigan player on hand to touch home the rebound, the ball came off the woodwork into his grateful arms.
It was a reprieve County took full advantage of just two minutes later, with Davies the supplier for Hughes who held off Antonio Amaya before slotting home underneath the advancing Stojkovic for his 20th goal of the season.
After a near-miss from Neal Bishop, Wigan's embarassment doubled in the 40th minute, sparked initially by a foul from captain-for-the-day Titus Bramble on Hughes.
From 25 yards out Davies curled home a superb right-foot free-kick that crept inside the right-hand post.
James McCarthy came close to pulling one back on the stroke of the break, only to strike the post from close range, adding to Wigan's first-half woe.
But for a stunning fingertip save to deny Hughes three minutes into the second half from Stojkovic, Wigan would have been dead and buried.
It was a much-needed turning point for Wigan because five minutes later they managed to haul themselves back into the tie.
Playing a one-two on the edge of the area with Rodallega, Scotland finished with aplomb by curling home his first goal for the club on his 21st appearance from 15 yards.
The £2million summer buy from Martinez's former club Swansea came within inches of adding a second via a 20 -yard drive soon after, before then being denied via Schmeichel from a close-range strike.
But County far from crumbled as they sought to take advantage of the gaps developing at the back, only for Hughes and 67th-minute substitute Luke Rodgers to find Stojkovic now in brilliant form.
His efforts were not in vain either as Wigan pressure eventually told in the 83rd minute when Watson headed home from close range after Bramble had knocked on a corner from 70th-minute sub Charles N'Zogbia.
Even then, though, County were not finished as Stojkovic underlined his ability with another fingertip stop in the dying moments after a Jackson corner had come off Wigan's Mohamed Diame.