No one was reported hurt in the incident, in which the plane carrying Indiana Governor and Republican vice presidential candidate Mike Pence came to rest in grass next to the runway after landing at New York's rain-soaked LaGuardia airport.
But with the mishap coming in the final throes of a combative campaign that will be decided November 8, several Twitter users described it as a metaphor for the 2016 race.
Trump, speaking in Ohio, said he was grateful that those on the plane avoided "grave, grave danger."
"I just spoke to Mike Pence. He's fine," Trump said.
Clinton also expressed relief that no one was hurt.
The former first lady and secretary of state enlisted the current first lady, who enjoys sky-high support, in hammering Trump and making the case for a third straight Democratic term in the White House.
Obama earned thunderous roars of approval from a crowd of 11,000 as she took the stage with Clinton in Winston-Salem, North Carolina, one of the swing states in play, where they accused Trump of seeking to depress turnout.
Obama has emerged as a compelling force in the hard-fought campaign, delivering powerful arguments against the Republican billionaire and in support of Clinton's bid to become the first female US president.
"She is ready to be commander-in-chief on Day 1, and yes, she happens to be a woman," Obama said of Clinton, whom she called "my girl."
The 52-year-old wife of President Barack Obama has energized Democrats by criticizing Trump for his strident rhetoric and for what she brands his "frightening" attitude towards women.
Trump's strategy was "to make this election so dirty and ugly that we don't want any part of it," she said.
"When you hear folks talking about a global conspiracy and saying that this election is 'rigged,' understand that they are trying to get you to stay home."
Clinton has basked in the results of new polls showing her with an impressive lead with just 12 days to go.
North Carolina voted for Obama in 2008, then for Republican nominee Mitt Romney in 2012.
But Clinton has expanded her narrow lead to 2.4 points in the southeastern state, where Republican leaders worry that Trump's slow collapse will hurt them in congressional races.
Clinton, whose campaign announced a large fundraising haul on Thursday, struck a tone of unity and optimism.
"As Michelle reminds us, this election is about our kids and, in my case, our grandkids," Clinton said. "Starting right now, let's come together. Let's work together and be hopeful and optimistic and unified."
