Brent crude prices rose to their highest in a year after Russia said it was ready to join a proposed deal to cap oil production in the hope of stemming a two-year price slide.
Sterling extended losses from Friday, when the British currency plunged to a 31-year low in what has been described as a "flash crash" event, reports Reuters.
A poll taken by CNN immediately following Sunday night's debate showed viewers said Clinton had beaten Donald Trump, 57 percent to 34 percent.
"The broader market is responding positively to the events over the weekend that make Clinton more likely to win," said Rick Meckler, president of hedge fund LibertyView Capital Management LLC in Jersey City, New Jersey.
Investors see a Democratic Clinton administration as more predictable than one led by Trump, who has provided less detail about his plans and raised fears of market volatility around his candidacy, Meckler said.
The Mexican peso, the largest emerging market currency in terms of trading volume, surged more than 2 percent against the U.S. dollar as markets trimmed chances of a Trump victory in November.
Trump, the Republican candidate, has vowed he would build a wall on the border with Mexico and renegotiate or scrap the North American Free Trade Agreement (NAFTA) if he is elected.
Stocks in Europe rose in tandem with the U.S. market. The pan-regional FTSEurofirst 300 .FTEU3 index rose 0.83 percent, while MSCI's all-country world equity index .MIWD00000PUS gained 0.54 percent.
The Dow Jones industrial average .DJI rose 135.36 points, or 0.74 percent, to 18,375.85. The S&P 500 .SPX gained 14.4 points, or 0.67 percent, to 2,168.14 and the Nasdaq Composite .IXIC added 42.83 points, or 0.81 percent, to 5,335.23.
The dollar firmed across the board as it continued to benefit from expectations the Federal Reserve would likely raise interest rates in December.
Investors are looking to Wednesday's release of minutes of the latest Federal Reserve Open Market Committee meeting to see how close the U.S. central bank was to hiking rates last month.
The dollar rose 0.78 percent against the yen to 103.70 yen JPY= and climbed against the euro, which fell 0.43 percent to $1.1151 EUR=. These gains pushed the dollar index up 0.18 percent at 96.809 .DXY.
Russian President Vladimir Putin said an output freeze or even a production cut were likely the only right decisions to maintain energy sector stability.
Global benchmark Brent crude futures LCOc1 reached the highest level since Oct. 9, 2015 at $53.73, before paring some gains to trade 2.68 percent higher at $$53.32.
U.S. futures CLc1 also gained, touching four-month highs, up 3.01 percent at $51.31 a barrel.
The U.S. bond market was closed for the Columbus Day holiday.