The Irish dominated the early possession but were hit on the break in the 14th minute, falling behind when Miroslav Stoch found space at the back post and made no mistake from close range.
O'Neill's men responded well and drew themselves level from the penalty spot after Shane Long was felled in the area by Slovakia goalkeeper Matus Kozacik. The Southampton striker stepped up himself and drilled the ball into the bottom corner to restore parity.
Ireland were ahead thanks to a second penalty kick moments later, again won by Long following a mistimed tackle from Liverpool's Martin Skrtel. This time Long handed the ball to James McClean, who beat Kozacik from 12 yards to make it 2-1 to the hosts.
The second half was a more subdued affair, with neither goalkeeper given much to do.
Darren Randolph had an easy save to make on the hour mark when Vittek gave his marker the slip and shot straight at the West Ham United keeper, while Robbie Brady thumped a free kick against the wall moments later.
Both sides attempted to force the other's hand with counter-attacking football for the remainder of the match, but ultimately cancelled each other out.