From 1-0 down, City's youngsters put three past Wolves at Aggborough Stadium to secure their place in the fourth round of the FA Youth Cup, with Jahmari Lindsay also on the scoresheet before late efforts from Richards and Grist.
The young Foxes arrived in Kidderminster full of fight and talent, with the starting line-up including Grist, Logan Briggs, and Trey Nyoni, who all made substitute appearances for the Development Squad only two days ago, when they were held to a goalless draw against Porto B in the Premier League International Cup.
Also involved in the proceedings was midfielder Will Alves, who only featured for the first team the day before, during the Foxes' 3-0 win against MK Dons in the Carabao Cup Fourth Round.
On a brisk night, it was the travelling side who were looking more likely to find an opening goal. Richards and Alves were at the fore-front of most Leicester's attacks.
Alves' skill was clear to see early on when quick feet allowed the playmaker to weave his way into the box, before trying to pick out a team-mate, but solid defending denied any goalscoring opportunity.
After a sustained period of pressure from the Foxes, it was the hosts who would strike first, when a deep cross from Temple Ojinnaka found its way through the City defence, and straight into the back of the net.
However, Leicester weren't to be trailing for long, when a well whipped cross was touched goalwards by Lindsay only minutes later, bringing the scores back level.
Following the two goals, both sides looked to threaten again, with neither producing any clear-cut chances before the referee's whistle called for half-time.
In the second half, tensions started to rise as both teams saw the chance of progression into the next round of the tournament, and it was the Foxes to go closest once more on the hour mark.
Midfielder Jayden Joseph tried his luck from outside the box and produced a sweet connection with the football, but the powerful effort ended up on the wrong side of James Storer's goal.
Less than 10 minutes later, City were in again. Goalscorer Lindsay produced an accurately delivered cross into the box, looking for Nyoni, but the striker could only look on helplessly as the ball flashed past, a yard in front of his path.
With six minutes additional time shown by the fourth official, Leicester started to pile on the pressure, and almost scored a winner with substitute Josh King, when he directed a strike towards goal, forcing a strong save from the Wolves 'keeper.
After 90 minutes of football, there was nothing to separate the sides, and the night would continue with extra-time, where City's pressure would pay off with two goals in 10 minutes.
Tricky midfielder Alves was once again at the heart of the action, weaving in between players in the home box, before Richards unleashed a left-footed effort past the helpless Storer into the net.
The Foxes' lead was soon doubled when a corner, not dealt with by the Wolves 'keeper, was tapped in by Grist at the back post, giving the travelling side a strong lead at the break in extra-time.
The final 15 minutes saw the Foxes remain in control, and with no response from Wolves' youngsters, they head into the fourth round of the cup, where they'll face Sheffield Wednesday in January.
Major moment – Winning it in extra-time
After 90 minutes of football, on a bitterly cold night in Kidderminster, Leicester came flying out of the traps at the start of extra-time, and settled the tie with two quick-fire goals from Amani Richards and Ben Grist.
Who impressed? – Skilful Will Alves
Will Alves' mesmerising dribbling ability is a joy to watch and Wednesday night was no different. Rarely beaten off the ball, the young midfielder was always looking to create an opening. A notable mention must also be given to Amani Richards, who found the net in extra-time to secure the win for the Foxes.
Where do we stand? – Into the fourth round
Following a successful night in Kidderminster, Leicester's Under-18s will travel to Sheffield Wednesday in the FA Youth Cup Fourth Round.
Coming up – Brighton (H)
City's Under-18s are next in action on Saturday 7 January (11am GMT kick-off) when they face Brighton & Hove Albion at LCFC Training Ground in U18 Premier League South.
The details...
City: Addai; Grist, McAlinney; Wilson-Brown; Joseph (Evans 62'), Briggs, Alves (T. Thomas 110') , Cartwright (c), Lindsay; Richards (Lewis 116'), Nyoni (King 86').
Subs not used: Cook, Weeks, Javaid.
Goals: Lindsay 25', Richards 93', Grist 100'.