Crude prices flirted with a break below $30 per barrel, before recovering slightly as investors booked profits. Benchmark Brent crude was up nearly 2 percent and U.S. crude gained 1.4 percent.
Nine of the 10 major S&P sectors were higher, led by the energy sector's 1.7 percent increase.
"The market is still very much in gripped by the plunge in oil prices and this morning we're seeing a slightly little better tone to oil prices," said Peter Cardillo, chief market economist at First Standard Financial in New York.
Apple was up 1.5 percent at $100.01 on Tuesday after BofA Merrill raised its rating on the stock to "buy". The stock gave the biggest to the S&P and the Nasdaq.
At 9:39 a.m. ET (1439 GMT), the Dow Jones industrial average was up 158.61 points, or 0.97 percent, at 16,557.18.
The S&P 500 was up 19.65 points, or 1.02 percent, at 1,943.32 and the Nasdaq Composite index was up 64.64 points, or 1.39 percent, at 4,702.63.
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U.S. stocks have opened higher in the past two sessions, only to reverse course later in volatile trading as investors fretted about a China-led global growth slowdown and sharp turns in oil prices.
Investors are bracing for a U.S. earnings recession, with fourth-quarter profits expected to decline for the second straight quarter.
But, Cardillo expects the gyrations in the oil markets will be topmost on investors' minds.
"I think earnings season this time is going to take a back seat because oil is still going to be the dominating factor for investors".
Health stocks also rose, after a steep fall on Monday, led by Celgene's 4 percent jump.
Anthem was up 4.1 percent at $133.64 after it raised its profit forecast for 2016. The news also boost fellow health insurers UnitedHealth, Aetna and Cigna, all up between 3-4 percent.
Intel rose 2.3 percent at $32.81 after JP Morgan resumed coverage of the stock with an "overweight" rating. Mizuho also raised its rating to "buy".
Apollo Education jumped 12.8 percent to $7.19 on reports that PE firm Apollo Global Management was in talks to buy the for-profit education provider.
Lululemon was up nearly 9 percent at $59.56 after the Canadian yogawear retailer raised its fourth-quarter revenue forecast.
Advancing issues outnumbered decliners on the NYSE by 2,287 to 467. On the Nasdaq, 1,922 issues rose and 366 fell.
The S&P 500 index showed no new 52-week highs and three new lows, while the Nasdaq recorded four new highs and 29 new lows.