POWER OF ATTORNEY

KNOW ALL MEN BY THESE PRESENTS:  That the undersigned has made, constituted and
appointed, and by this instrument does make, constitute and appoint, each of
MARK M. McGUIRE, THOMAS E. MORAN, LIZBETH L. WRIGHT, SUZANNE K. HANSELMAN,
KATHLEEN S. O'CONNOR AND ELIZABETH K. RIOTTE, acting individually, as his or her
true and lawful attorney, for him or her, and in his or her name, place and
stead, to affix, as attorney-in-fact, the signature of the undersigned to
reports to the Securities and Exchange Commission on Form ID and reports on
Forms 3, 4, 5 or 144 with respect to transactions or holdings by the undersigned
in equity securities issued by Eaton Corporation plc, a public limited company
incorporated in Ireland ("Eaton"), and to any and all amendments to such
reports, giving and granting unto each such attorney-in-fact full power and
authority to do and performance every act and thing whatsoever necessary to be
done in the premises, as fully as the undersigned might or could do if
personally present, hereby ratifying and confirming all that each such
attorney-in-fact shall lawfully do or cause to be done by virtue hereof.

        This Power of Attorney shall revoke any Power of Attorney previously
executed by the undersigned regarding the filing of Forms 3, 4, 5 or 144 with
the Securities and Exchange Commission for transactions in Eaton securities, but
this revocation does not invalidate any actions taken pursuant to any prior
Powers of Attorney.

        This Power of Attorney shall expire on the date the undersigned is no
longer required to file Form 3, 4, 5 or 144 reports with the Securities and
Exchange Commission with respect to holdings of and transactions in securities
issued by Eaton, unless revoked in writing prior thereto.

        IN WITNESS WHEREOF, this Power of Attorney has been signed at Darien,
Connecticut, this 9th day of November 2012.

                                        /s/ Michael J. Critelli
                                        ----------------------------------------
                                        Michael J. Critelli