After that Ulster take on current RaboDirect PRO12 leaders Leinster before finishing their regular season campaign off against European Cup semi-finallists Munster.
And although Ulster couldn't have asked for a much harder run in, prop Lutton insists there is no need for anyone at Ravenhill to panic.
"We've three games - win those and we're in a semi-final," Lutton told the Belfast Telegraph. "It's a simple enough equation for us really; it's in our own hands.
"Admittedly it's a lot easier said than done because those are three really tough games. But if we approach them one at a time and look at each game individually you see that they're all winnable.
"We're going to Glasgow looking to get the win and then we have a week off to rest the bodies before coming back the following Monday ready to tackle those two inter-pros".
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Guinness PRO12 Ulster News
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