Rhodes suffered what manager Gordon Strachan described as a 'freek leg injury' while Phillips pulled out with a tight hamstring.
Leeds striker Ross McCormack was drafted in as a replacement for Rhodes and arrived in Glasgow full of confidence having scored six goals in his last two league games for the Elland Road side.
"I have spoken with his manager Brian McDermott this morning and they are very pleased with him," said Strachan.
"He has just had a wee change of positional play at Leeds which Brian thinks has helped him to score more goals and we will take that on board as well."
Scotland take on Jurgen Klinsmann's side at Hampden on Friday before travelling to Oslo to face the Norwegians next Tuesday.
And you can keep up to date with the action on Friday from 7.30pm live on Sky Sports 4