After opening with an eight under par 64, Swede Noren added further birdies at the two par fives on the front nine - the third and fifth - to be ten under for the week after 27 holes.
But 21 year old Northern Irishman McIlroy, just five days after his Masters Tournament disappointment, took over the chase of the leader with Italian teenager Matteo Manassero among the afternoon starters.
Starting his second round at the tenth, World Number Nine McIlroy fired off five birdies in an outward 31 to advance to eight under for the week.
Manassero was joined in a share of third place by Scotland's Stephen Gallacher, who was one under par seven holes into his round.
World Number One Martin Kaymer was one under for the day and three under for the tournament through nine.
Like Manassero, Open Champion Louis Oosthuizen and newly-crowned Masters Tournament winner Charl Schwartzel were teeing off later in the day - with the latter probably needing a sub-par round to make the cut.