The 32-year-old Republic of Ireland skipper helped to maintain his country's bid for a ticket to Brazil next summer with a hat-trick in Friday night's Group C victory over the Faroe Islands at the Aviva Stadium. That, coupled with Austria's win over Sweden, left the pair locked together on 11 points behind leaders Germany.
It has always looked like a three-way battle for second place, and that means Sweden's trip to Dublin in September and Ireland's visit to Austria four days later are likely to have a decisive say in the outcome, and Keane said: "We know what we have to do: we have to play those two in September, so those two games are very, very crucial and will probably make or break us."
He added: "All we have to do now is just concentrate on ourselves and not worry too much about Austria or Sweden.
"These games give you confidence. It's always good coming into the next qualifier when you have just come off a good win and after getting three points.
"We will certainly look forward to those two games. They are two games that we have to win to stay in contention.
"We have got a good chance, there's no question. We have got Sweden at home and Austria away, and we are quite capable of going to Austria and getting three points."
Friday night's win extended the Republic's impressive end-of-season form after a draw in England and last Sunday's demolition of Georgia. They have now played eight times since they were humbled 6-1 by the Germans on their own pitch in October last year and lost only once, and that is a source of some encouragement for their captain.
Keane said: "I don't think anyone had any doubt about it, to be totally honest with you. People forget, we played against probably one of the top three teams in the world in Germany.
"The manner in which we were beaten, it wasn't good because of the way we set ourselves out and the pride we have, and it wasn't good enough. But the good thing about football is there's always another game and it's about bouncing back and not being a baby sitting in a corner and crying about it."