ENGLISH CLASS | Stills from the 1998 video on the left; the Hurwitz sisters at right.

Alanis Morissette's 1996 hit song "Ironic" has agitated rhetoric snobs for years. Taking listeners through a series of unlucky coincidences—a rainy wedding, a no-smoking sign on a cigarette break, a failure to take good advice—the Grammy-nominated song is devoid of any literal irony.

In July, a pair of 24-year-old sisters from North Haven, Conn., rewrote the lyrics and recorded a shot-by-shot parody of the original music video. Rachael and Eliza Hurwitz's new version, "It's Finally Ironic," has been viewed on YouTube more than half a million times. "We fixed it for you, Alanis," Eliza coos in the spoof. "You're welcome."

The concept of irony has a way of befuddling people. Over the years, the word has come to be widely misused as a synonym for "unfortunate." By definition, though, irony implies that something has happened in the opposite way from which it was intended. "Rain on your wedding day is just bad luck," said Ralph Sneeden, an English teacher at Phillips Exeter Academy in New Hampshire.

Ms. Morissette has since claimed that the irony of the song lies in its lack thereof, but the Hurwitzes took a more direct approach, reworking each original verse to one that indisputably qualifies as ironic. "It's a black fly in your Chardonnay, that was specifically purchased to repel black flies," goes the rewrite. "It's like rain on your wedding day—a day and place you chose because it's known not to rain."

Eliza and Rachael Hurwitz are two of a set of triplets who remembered hearing an English teacher bemoan the song's lyrics. Eliza, a stand-up comedian who recently graduated from New York University, decided to rewrite the song last year while writing a column for the humor website Hello Giggles.

She enlisted Rachael, a recent Connecticut College graduate who is now pursuing a career in music, to film a spoof with her. The sisters live in New York and began performing comedy together this summer. This was their first comedy video.

"We felt like [a video] would pack the most punch," Eliza said. "We were hoping we'd get a couple hundred views, but then ['Star Trek' actor] George Takei tweeted about it and it just blew up." The sisters said they plan to move away from parody and focus on original content in their next videos.

Ms. Morissette's original song is no stranger to ridicule. Shortly after its debut, Irish comedian Ed Byrne ruthlessly roasted the lyrics in his routine. "The song should have been called 'Unfortunate,' " he ranted. "There's nothing ironic about being stuck in a traffic jam when you're already late for something, not unless you're a town planner."

A decade later, writer Patrick Cassels rewrote a few of the lyrics in a list-style format for College Humor. Mr. Cassels also aimed for real irony—it's like "rain on your wedding day...to Ra, the Egyptian sun god," he wrote.

His post didn't exactly go viral. "The girls bring a lot more to it than I did," he said. "Their version is way more multidimensional."

The Original: 'Ironic' by Alanis Morisette

The Parody: 'It's Finally Ironic' by Eliza and Rachael Hurwitz

Write to Megan Buerger at megan.buerger@wsj.com