If you have a radio controlled clock or watch then click to confirm your bid EXACTLY one second before the auction closes. That way your bid ends up tagged with the same time as the auction close. And remember, always bid the maximum amount that you are willing to pay and NOT the amount shown as the minimum bid the last time you looked - others will be doing the same.
I'm not sure why eBay doesn't extend auctions for at least 10 minutes after a bid. I have a vague recollection that they used to. Perhaps they could list it as, yet another, charged-for service.