The visitors had earlier lost goalkeeper Andy Carlin who was giving his marching orders for bringing down Paul McManus in a goalscoring opportunity inside the box.
They fought back well from the set back and Richie's header gave him the result they deserved.
Early Richie saw a shot a rebound of the bar following a David Williams corner in the 20th minute.
However, Cowdenbeath were not denied for long as they were awarded a penalty following a Danny Black foul on Darren Gribben.
Rovers keeper Chris Fahey produced an excellent save to deny Liam Buchanan from the resulting spot kick but Williams was on hand to turn in the rebound.
It did not take Rovers long to get back on level terms following Carlin's foul on McManus.
The Rovers striker got up and dusted himself down before sending substitute keeper Alan Fleming the wrong way from the spot.
Just before half time Albion almost got in front when Fleming produced an excellent save to deny Graeme McLaren.
Rovers did take the lead early in the second half when Fleming flapped at Jered Stirling's free-kick and James Mercer was on hand to head the ball home.
Four minutes later Cowdenbeath were back on level terms as a Black slip let Gribben through on goal and his shot looked to be heading home but Williams was on hand to tap in.
Both sides tried hard to grab the winner in the latter stages in the second half and it wasn't until the last minute when a Williams corner was met by Ritchie at the near post.