A Clinton presidency would be more positive for the markets because her positions are more well known than those of her Republican rival Donald Trump, according to a Reuters poll.
A CNN/ORC snap poll of debate watchers found that 57 percent thought Clinton won the encounter, versus 34 percent for Trump.
Oil prices rose 2.8 percent and touched their one-year high as speculators raised bets that prices would gain on the back of an agreement among OPEC producers to rein in record output levels.
"Investors will ponder the presidential debate and follow the events in the commodity markets, especially oil," said Peter Cardillo, chief market economist at First Standard Financial in New York.
Investors are also bracing for the third-quarter earnings season, which unofficially kicks off on Tuesday when aluminum producer Alcoa (AA.N) reports.
"The markets seem to be looking for a repeat of last quarter, with most companies exceeding Street consensus but obviously on a scaled back earnings growth," Cardillo said.
Earnings of S&P 500 companies are expected to drop 0.7 percent, according to Thomson Reuters data.
The dollar .DXY, which has been swinging between gains and losses for the past five trading days, was up 0.2 percent against a basket of major currencies. The pound GBP=fell again on Monday.
The U.S. bond market was closed for the Columbus Day holiday.
At 9:39 a.m. ET (1339 GMT), the Dow Jones Industrial Average .DJI was up 127.61 points, or 0.7 percent, at 18,368.1.
The S&P 500 .SPX was up 12.42 points, or 0.58 percent, at 2,166.16 and the Nasdaq Composite .IXIC was up 34.29 points, or 0.65 percent, at 5,326.70.
Ten of the 11 major S&P 500 indexes were higher, led by a 1.36 percent rise in the energy sector .SPNY. Telecom service providers .SPLRL were the lone losers.
Exxon (XOM.N) and Chevron (CVX.N) were among the top influences on the S&P and the Dow.
Twitter dropped 12.3 percent after Bloomberg reported on Saturday that "top potential bidders" had lost interest in the company.
Mylan was the top gainer on the S&P, rising 11.4 percent. The drugmaker on Friday said it would pay $465 million to settle questions over whether it underpaid U.S. government healthcare programs by misclassifying its EpiPen emergency allergy treatment.
Merck rose 2.1 percent after clinical data showed its Keytruda immunotherapy offered big benefits in previously untreated lung cancer patients, either when given on its own or with chemotherapy.
Advancing issues outnumbered decliners on the NYSE by 2,314 to 369. On the Nasdaq, 1,795 issues rose and 426 fell.
The S&P 500 index showed 15 new 52-week highs and one new lows, while the Nasdaq recorded 56 new highs and seven new lows.