Some dictionaries gloss utilize as using something for a purpose that it is not normally employed for. But prescriptive grammarians are pretty clear on such use. Fowler in Modern English Usage (p670) says:
If differentiation were possible between utilize and use it would
be that utilize has the special meaning of make good use of,
especially of something that was not intended for the purpose but will
serve. But this distinction has disappeared beyond recall; utilize
is now ordinarily treated as a LONG VARIANT of use. A form is
enclosed herewith for favour of your utilization is an example of the
pretentious diction that prefers the long word.
Partidge in Usage and Abusage (p343) is typically blunt:
utilize is, 99 times out of 100, much inferior to use; the other one time it is merely inferior.
And here is the more contemporary Grammar Girl's similar take on the issue: http://www.quickanddirtytips.com/education/grammar/use-versus-utilize
Nevertheless, this Usage Note from TheFreeDictionary indicates when utilize might indeed be the better choice:
A number of critics have remarked that utilize is an unnecessary
substitute for use. It is true that many occurrences of utilize could
be replaced by use with no loss to anything but pretentiousness, for
example, in sentences such as They utilized questionable methods in
their analysis or We hope that many commuters will continue to utilize
mass transit after the bridge has reopened. But utilize can mean "to
find a profitable or practical use for." Thus the sentence The
teachers were unable to use the new computers might mean only that the
teachers were unable to operate the computers, whereas The teachers
were unable to utilize the new computers suggests that the teachers
could not find ways to employ the computers in instruction.