Ritchie took over at Oakwell following the departure of Paul Hart and has masterminded a five-match unbeaten run which has seen Barnsley move towards the fringes of the play-off race.
They appeared to be coasting against a Walsall side that arrived without a win in nine games.
A first-half strike from centre-back Antony Kay and an early second-half goal from on-loan striker Daniel Nardiello had seen Ritchie's men cruise into a thoroughly deserved 2-0 lead but as so often has happened this season Barnsley shot themselves in the foot.
They allowed Walsall to hit back with two goals in as many minutes.
Inspired by player-manager Paul Merson, the visitors cut the deficit on 51 minutes when a mistake by Kay enabled Julian Joachim to scamper clear and rifle the ball beyond young keeper Scott Flinders.
A minute later it was 2-2. Barnsley defender Bobby Hassell was booked for a foul wide on the left and the resulting free-kick was headed in from less than six yards by striker Jorge Leitao.
The Tykes, to their credit, were immediately back on the attack but Walsall keeper Andy Oakes twice denied the lively Chris Shuker.
Eleven minutes from time Walsall centre-back Neil Emblen was penalised for his challenge on Michael Chopra, with the referee pointing to the spot.
Chopra had missed at league leaders Luton two days earlier and did the same again here, smashing his spot-kick against the bar.
But just a minute later Chopra was all smiles when he turned in a low cross from substitute Simon Johnson to register his 16th goal of the season.