The greatest weight on the Dow was Disney. Shares of the firm closed down about 1 percent, continuing to decline after BTIG downgraded the stock Friday, despite a record opening weekend for the latest "Star Wars" movie in North America. The stock is up 13 percent for the year so far.
The Nasdaq composite outperformed the major averages with a gain of nearly 1 percent, helped by a 1.2 percent gain in Apple. The Market Vectors Semiconductor ETF (SMH) closed up 1.77 percent, for its best day since Nov. 6.
"I think it's really just a test to see if the equity market can advance in the backdrop of low energy prices," said Jack Ablin, chief investment officer at BMO Private Bank.
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Energy eked out a positive close after holding mostly lower under pressure from oil's continued decline. Energy is down more than 20 percent year-to-date as the worst S&P performer.
The Alerian MLP ETF (AMLP) jumped 4.3 percent. Natural gas bounced from near multi-year lows to settle up 8.15 percent for its largest one-day gain since Oct. 27.
WTI crude futures for January delivery settled up 1 cent at $34.74 a barrel after earlier dipping below $34 to hit a fresh near-seven-year low. The contract expired Monday.
The February contract did not touch new lows, and settled down 25 cents at $35.81.
"It's not like oil is directly responsible for why stocks dropped last week. The market is clearly concerned about global economic fundamentals," said Pavel Molchanov, energy analyst at Raymond James. He expects oil to recover to around $60 a barrel in the second half of next year.
Brent settled higher at $36.35 a barrel, after hitting $36.04 a barrel, its lowest since July 2004.
The Dow transports closed about 0.7 percent higher, with airlines leading advancers.
"This could be a dead cat bounce after the action on Friday. You could see some seasonality push it higher. ... It all depends if we can hold that low from Friday," said John Caruso, senior market strategist at RJO Futures.
U.S. stocks closed more than 1.5 percent lower Friday near session lows, wiping out gains for last week, as investors weighed low oil and economic data in the aftermath of the Federal Reserve's rate hike Wednesday. Options expiration also contributed to volatility, with trade volume the second-highest of the year.
Both the S&P 500 and Dow Jones industrial average are still negative year-to-date, down more than 1.5 percent and 3 percent, respectively.
With less than 2 weeks to the end of the year, U.S. equities kicked off the shortened holiday week with gains. The U.S. stock market closes early Thursday, Christmas Eve, and is shut on Friday for Christmas Day.
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"To me this just has to do with end of the year. Normal seasonal bounce. We'll see if it can last," said Adam Sarhan, CEO of Sarhan Capital.
"The market's oversold. It's overdue for a bounce. I think it's more of a rotation going on underneath the surface because leadership is very narrow," he said.
Analysts also noted some support for gains in stocks from the weaker U.S. dollar, which held slightly lower against major world currencies, with the euro above $1.09. The yen was near 121.16 yen against the greenback.
Earlier, the U.S. dollar index extended losses after the Chicago Fed National Activity Index showed a decline to minus 0.30 in November from minus 0.17 in October.
No other major economic data was due Monday, while third-quarter GDP is expected Tuesday and personal income data is due Wednesday.
Treasury yields held little changed, with the 2-year yield near 0.95 percent and the 10-year yield around 2.19 percent in the close.
"Even though the (Federal Reserve) did move off the zero bound, it did so in light of an economy that shows little signs of accelerating," Luschini said.
"On balance the Fed is unwilling to be as aggressive despite what their own dot plot would suggest," he said.
Atlanta Fed President Dennis Lockhart said Monday the Federal Reserve's promise of gradual rate hikes in coming months means the central bank will not raise rates at every meeting, according to a WABE radio report cited by Reuters.
Lockhart will not be part of the Federal Open Market Committee in 2016.