Keane spot-kick saved as Ireland draw
Ireland opened the scoring after 16 minutes when Sean St. Ledger scored off a rebound before Slovakia's Jan Durica levelled 20 minutes later, heading in a deflected corner kick.
Mucha then brought down Aiden McGeady in the box a minute before half-time but redeemed himself by stopping Keane's penalty.
However, Slovakia were unable to carry momentum into the second half and managed only two shots on target to Ireland's three.
The Slovaks, who beat defending champions Italy 3-2 in the first round of the World Cup in June, were coming off a shock 3-1 defeat to Armenia on Friday.
The team has seven points from four matches so far, level with Ireland and one point behind group leaders Russia.