Rock-Paper Switch

Basically have a team of heroes face off against a team of villains where each hero pairs off with another villain, mano a mano. In some cases, it's their enemy rivals and in some cases the heroes are fighting off their evil counterparts (which invariably leads to starting off with everyone fighting themselves). This unfortunately leads to potential complications, as usually the one they're fighting against has the upper hand, because being their rival means knowing their moves and how to counter it.

So in a stroke of obvious brilliance, have the heroes trade enemies. This leads to quick defeat as now the heroes are fighting to their strengths, and the matches are one by one brought to a close.

The degree of Genre Blindness which affects teams presented with their evil copies is amazing. They have to let themselves get smacked around excessively before coming up with this, and they always say it like it's not always the answer to this particular plot complication.

Examples of Rock-Paper Switch include:

Anime and Manga

Inverted in an episode of Bleach. Uryuu fairs poorly against a Smash Mook, while Chad has trouble with a fast and agile Arrancar. They switch opponents and Beat Them At Their Own Game.

Comic Books

An early Archie Sonic the Hedgehog comic had the Freedom Fighter's beating their evil selves from another dimension like this.
The old X-Men comics used this a lot. There were always mooks whose Applied Phlebotinum allowed each mook to completely counter the powers of one certain X Man apiece... so the X Men switched sparring partners. and it never dawns on the mooks to develop the ability to counter the powers of multiple X Men at a time.
- Also done in a later episode of the '90s animated series, where some of the X-Men are facing X-Factor and having a stalemate (Cyclops vs. Havok; Wolverine vs. Multiple Man; Beast vs. Wolfsbane; etc.). The X-Men switch it up and get the upper hand.

Literature

Sūn Bìn's trick (see Real Life below) is almost exactly replicated in one Piers Anthony's Battle Circle books, albeit involving fighters. They then start discussing what happens when the other side is as Genre Savvy, or it's uncertain who's the best, etc.

Live-Action TV

In Power Rangers, this happened with the original Psycho Rangers - all the rangers dressed as the Blue Ranger to confuse them.
Something like this occurred in the Star Trek: The Original Series episode "That Which Survives". A computer generated construct had the power to kill a specific human target by touch. When the Enterprise crew members facing it realized this, they interposed someone else between the opponent and its target, foiling the attack. Eventually the computer wised up and created a construct for each crew member, so the crew switched around until each was facing a construct meant for someone else.

Web Comics

The Order of the Stick had a villain version, as well as subverting it, when Nale traded enemies with Thog, only to end up with a worse match-off.

"I've wanted to beat the crap out of someone who looks just like you for a long time."

The Dubious Company teams of start off running at their Evil Counterpart during the showdown in Kreedor's castle, only to trade up immediately for defensive or vendetta reasons. It ends with Sal vs Izor, Walter vs Mary, Tiren vs Gary, Elly vs Marty, and Leeroy vs Sue.

Western Animation

An episode of Buzz Lightyear of Star Command had the heroes each take advantage of a teammate's clone this way (for instance, "Feara" believed she was chasing Mira using her intangibility powers, which wear her out, but she was actually chasing a hologram by XR, causing Feara to be the one to wear out.)
The Extreme Ghostbusters cartoon had an episode in which the characters were trying to defeat their worst fears. They fail, and suddenly decide to switch and fight each others' fears.
Justice League Unlimited had this when the seven heroes went up against Brainithor. This had Wonder Woman and Superman trading off, as well as Hawk Girl and Green Lantern.
An episode of the Powerpuff Girls had them facing impostors in Paper Thin Disguises, which nonetheless fooled the girls (and the crooks) into attacking each other until they got the idea to only attack their own counterpart—the inverse of the trope.
The episode "Wizards, Warriors, and a Word From Our Sponsors" of ReBoot had Mike and Dot trade against their evil counterparts and quickly winning.
Season Four finale of Teen Titans when Trigon created evil duplicates of Starfire, Cyborg, and Beast Boy. Beast Boy took on Evil Starfire, Cyborg took on Evil Beast Boy, and Starfire took on Evil Cyborg.
Xiaolin Showdown did the same thing.

Real Life

Older Than Feudalism. Sun Tzu's descendant Sūn Bìn reportedly advised a variant of this in a series of horse races in the mid-4th century BCE: "Match your third string against his first, your best against his second, and your second best against his weakest." So they won two out of three races and cleaned up on the betting.
This is considered unsportsmanly at best in high school tennis leagues.