United are unbeaten in eight games and have won five of their last six, drawing 2-2 with Motherwell at Tannadice earlier this month.
However, Houston's side have a less than convincing record against Motherwell this season and lost at Fir Park in the Co-operative Insurance Cup in October.
"Going to Fir Park has never been easy and our record there this season is that we've lost two, so we've got a lot to work on and a lot to play for," Houston told STV.
"We need to be prepared maybe even for extra time and penalties."
Source: PA
Source: PA