The Saints beat Worcester Warriors 42-14 at Franklin's Gardens this afternoon to secure fourth place in the table, but now face a trip to The Stoop to take on Conor O'Shea's first-place Quins.
"I think we've got a good chance," Mallinder told Sky Sports News.
"It's been an inconsistent season, but we had a cracking win down at Exeter last week.
"Harlequins will be going in full of confidence, and deserve to be top, but we know we've got a good team and we'll go there knowing we can win."
Meanwhile, Quins wrapped-up their regular season with a 24-10 win at Sale.