Liam Lawrence telegraphed a delighted corner kick towards the near post on 14 minutes which the left-back met with a beautiful header to glide in the opener of a 3-1 victory.
The win followed Ireland's 1-0 victory away to Armenia last week and secured maximum points from the opening pair of European Championship qualification fixtures.
"It was nice to score of course, particularly getting us off the mark as well, but the main thing was getting the three points to build on the Armenia result," said the 33-year-old.
"All three were great goals. Robbie Keane took his well, Kevin Doyle's was a tremendous strike - a great finish - so there were three really great goals after mine.
"Shay couldn't really do much about their goal. You can't really do much like things like that in football, a shot from 25 yards.
"Once we got the third I thought we could have got more - but I think we have to be happy with the 3-1 result really."
News of Slovakia's 1-0 win in Moscow over the group's top seeds, Russia, earlier in the day filtered through the Irish camp before they took to the field for their assignment.
Next up for Ireland is the visit of Dick Advokaat's Russia to Aviva on October 8, when Kilbane reckons his side won't let up in their quest to see out the campaign in top spot.
"Russia will be a little hurt from losing the home game but we won't take them for granted. We'll feel confident of winning the game though," he said.
"Slovakia have made a brilliant start with two wins and are going to be difficult to overhaul. This will be a tough campaign but we've given ourselves a right good chance of going on and qualifying for the Euros in 2012."
Ireland defeat Andorra more convincingly than the 3-1 scoreline suggests ...
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