Following Anders Dreyer’s opener for the Seagulls in the 35th minute, a headed double from Wright either side of the interval turned the match on its head before Aaron Connelly's late equaliser.
City’s line-up featured four changes from the 1-1 draw with Chelsea with Danny Simpson, Louis Ramsay, Raúl Uche Rubio and Wright coming in at Holmes Park.
Callum Elder also started for the Foxes in Whetstone after signing a new deal with the Club while injured Layton Ndukwu, Sam Hughes, Admiral Muskwe and Josh Eppiah sat it out.
Brighton, who had Colombia international Jose Izquierdo among their ranks, went close early on as Alex Cochrane crossed for Connelly, but the Seagulls man headed it just wide.
There was also an audacious effort from Viktor Gyökeres, which City ‘keeper Viktor Johansson will have been relieved to see fly just over inside the opening 10 minutes.
Midway through the first half, it landed perfectly for Kiernan Dewsbury-Hall to unleash a wicked shot at goal, forcing Hugo Keto into an outstanding save, and while it fell to Uche Rubio, the Spaniard was adjudged to have strayed offside before he nodded the deflection in.
But it was the visitors who took the lead after 35 minutes as Dreyer’s long-range effort deflected off Josh Knight and into Johansson’s bottom corner.
City, though, rallied quickly and went into the break level as Wright’s leap and header, inside the Brighton six-yard box, was rewarded with his first goal of the 2018/19 season.
Just seven minutes into the second half, Wright once again rose highest to nod Elder’s cross into the bottom corner, making the score 2-1 and seemingly sending the hosts on their way to victory.
With seconds remaining, however, up stepped Connelly to lash home Brighton's equaliser and seal a share of the points for the south coast outfit.
Who impressed?
Back in the team for the visit of Brighton, former Blackburn Rovers forward Callum Wright seized his opportunity to impress with a brace of goals in Whetstone.
Wright was a constant menace for the visitors and got his due reward with two goals which will last long in the memory for the 18-year-old.
Where does it leave us?
The Foxes are up to third in Premier League 2 Division 1 summit on 11 points, level with leaders Everton, with a goal difference of +5.
Coming up…
City’s youngsters next host Arsenal at Holmes Park on Monday 1 October in Premier League 2 (7pm BST kick-off) – a fixture you can watch live on LCFC TV.
The details…
City: Johansson, Simpson, Elder, Dewsbury-Hall, Knight, Johnson, Ramsay (Kaba Sherif 77), King, Loft, Uche Rubio (Leshabela 66), Wright (Martis 83)
Subs not used: Pascanu, Davies
Attendance: 252