A phrase for: an underhanded malicious act that appears to be done in good faith

It sounds like a spite:

• a malicious, usually petty desire to harm, annoy, or humiliate another person; malice.

• malevolence by virtue of being malicious or spiteful or nasty.

The expression is out of spite :

• with the desire to harm someone or something.
  • Jane told some evil gossip about Bill out of spite. That was not an accident! You did it out of spite.

The Free Dictionary

Consider,

play a dirty trick on someone

play a trick on someone or play a prank on someone: to do a trick that affects someone. McGraw-Hill Dictionary of American Idioms and Phrasal Verbs

pull a dirty trick on someone

pull a trick (also, pull a stunt) [on someone]: to deceive someone; to play a trick on someone. McGraw-Hill Dictionary of American Idioms and Phrasal Verbs

screw someone over

: informal treat someone unfairly; cheat or swindle someone. OED

land [give] someone a low blow

low blow: an unfair blow McGraw-Hill's Dictionary of American Slang and Colloquial Expressions

For example, When my roommate moved out without a word of warning, leaving me to pay the entire rent, that was a low blow, or She wanted to win the argument, but bringing up his failed marriage was a low blow.

throw a [monkey] wrench in/into [the works]

: sabotage or frustrate a project or plans, as in The boss threw a monkey wrench into our plans when he said we'd have to work Saturday. This transfer of industrial sabotage—that is, throwing a tool inside machinery—to other subjects dates from the early 1900s.The American Heritage® Idioms Dictionary

Consider the following idioms:

do the dirty on someone:

to ​behave unfairly towards someone, usually without ​their ​knowledge

(http://dictionary.cambridge.org/dictionary/english/do-the-dirty-on-sb)

do someone dirt:

to do ill to someone; to harm someone’s reputation.

(http://idioms.thefreedictionary.com/do+someone+dirt)

do a dirty trick on someone:

dirty trick: an unkind or aggressive trick

(WordNet)

In addition, the British idiom to queer somebody's pitch could work:

to spoil someone's chances of doing something
She queered my pitch by asking for promotion before I did.

For instance, you could use "queer the pitch" in your political opponent example.

Follow a faulty order to the dot, making sure to give credit for the disastrous outcome where it's due. Possibly even (unofficially) suggest that course of action in the first place.

This is referred to as "malicious compliance".

https://en.wikipedia.org/wiki/Malicious_compliance