from what I know, the H1B rules were tweaked last year(?) so that people who got their H1B approved will not be deemed out of status even if their current status was set to expire before October 1st (H1B start date every year). someone please verify this.

Also, like Poon-hill stated, the 60 days grace period should cover it, even if what i said above was not true. confirm with a reliable source (best bet is the USCIS website www.uscis.gov  or the instruction pdf for H1B application).