Rain brought an end to play on Friday with McIlroy two shots clear of the cut after going four under following a horrific opening round 78 left him six over par.
The Northern Irishman appeared a real doubt to make the cut which was projected initially at two over but was later revised to three.
Two birdies in the first six holes raised McIlroy's chances and although he dropped a shot at the eighth, three further birdies boosted his hopes, just a week after he failed to make the cut at the BMW PGA Championship.
"I played better. I played much better," McIlroy said on the PGA Tour website. "Yesterday it was funny, I was just a little off, my concentration just wasn't really there.
"Today I really focused and saw my shots a lot better. And I played nicely so far. I need to continue to keep that going. ... The major goal today was to try to make it into the weekend. I'm on the right track to do that."
World number one Tiger Woods did make the cut despite a a miserable start to the day after a decidedly average first-round 71.
Teeing off on the back nine, the five-time tournament winner hit a double bogey and a bogey and Woods' non-appearance over the final two rounds became a real prospect.
Two birdies gave him some breathing space but a bogey at the last saw him finish with a two-over-par 74.
In stark contrast, leader Haas has shown impressive consistency over the two opening rounds with the American adding the 67 to his opening 68.
Haas started the day in a tie for seventh with Matt Kuchar and he returned to the Dublin course in red-hot form.
An eagle and two birdies on the front nine was followed by three more birdies and just one bogey until the final hole when he dropped a shot to shoot a 68 and move to nine under overall.
That bogey on the last could have offered a chink of light to Kuchar who, starting on the back nine, had overcome dropping a shot on the 14th by hitting four birdies.
However, he also hit a bogey on his final hole to finish with a two-under-par 70, three shots behind his fellow American.
Overnight leader Charl Schwartzel had a superb opening round of 65 including 10 birdies.
However, he could not in any way replicate that today.
The South African hit a double bogey on the ninth a bogey on the 11th before birdies on 11 and 14 meant he was in second, with three holes of his second round still to play.
Level with Schwartzel at six under is American Kyle Stanley is also at six under, recovering from a bogey at the first with birdies at seven and 11.
Bubba Watson was the big mover of the day with a stunning five under round which included six birdies, with his only blemish coming at the par three fourth.