The Tottenham full-back has recently recovered from hernia surgery and was a major doubt for the Kaunas clash when Craig Levein named his squad.
But, while Levein has lost other full-backs Lee Wallace and Kevin McNaughton through injury, Hutton proved his fitness and willingness in training before Scotland flew out to Lithuania on Wednesday afternoon.
"He has never missed a training session and in fact is looking really sharp and quick for the operation he had on his hernia not so long ago," said assistant boss Houston. "He has been buzzing and it was him who said he was desperate to be here.
"People in the newspapers were maybe ruling him out but he is very, very keen and in training he looks as if he has never had any operation in the last few weeks."
Houston believes the whole squad has trained with an added intensity ahead of Levein's first competitive game in charge.
The Scots beat the Czech Republic in March but lost 3-0 in Sweden last month.
"There is always an edge to a very important qualifier and I see the edge in training because the standard has been absolutely fantastic," the Dundee United manager said. "There are quality players in the side and we have got to make sure we go out there with confidence and pass the ball, retain the ball.
"We have to stop conceding goals and in Sweden we had a very young back four. We have more experience in there now."