Technology and Internet leaders stole earnings headlines on Thursday, and results prompted sharp movements in stock prices. Amazon popped after blowing away Wall Street estimates for earnings, while Google's price resisted largely disappointing results.

Alibaba, on the other hand, slid after missing expectations. CNBC's "Fast Money" traders, like investors in the wider markets, were split on how to play the companies.

Google's Class C stock jumped about 2 percent over $520 per share in after-hours trading despite its earnings and revenue missing analysts' expectations. The company is "habitually known for missing," said trader Steve Grasso.

Read MoreGoogle misses on earnings, blames strong dollar

A flush in price could soon test shareholders' commitment, he said. But Grasso, who owns Google stock, believes investors should look past short-term fluctuations.

"I do believe your longer-term investment in Google is going to be solid," he said.

Price movement in extended trading was "encouraging" for the stock, said trader Guy Adami. Trader Brian Kelly called it "a little bit of a pop" but added that he doesn't "think you buy this thing."

Shares shot more than 14 percent higher in extended trading after the e-commerce giant easily topped Wall Street expectations. Amazon cited strong holiday sales and growth in its Prime service.

Read MoreAmazon earnings: 45 cents a share vs. expected EPS of 17 cents

The boost might provide an opportunity to cash in on the stock, Adami said.

"I'm in the taking-profits camp here," he said.

Trader Dan Nathan also expressed skepticism about jumping into the stock on Thursday, when it climbed above $350 per share.

"Don't chase it here at $350," Nathan said.

Alibaba shares fell nearly 9 percent on Thursday after the Chinese e-commerce company fell short of analysts' expectations for revenue. "You absolutely buy it" on the drop, Kelly said.

Read MoreAlibaba's magic fades as stock plunges

Nathan didn't share the sentiment, saying selling at the current level around $90 per share would be a good move.

Disclosures:

Guy Adami

Guy Adami is long CELG, EXAS and INTC. Guy Adami's wife, Linda Snow, works at Merck.

Brian Kelly

Brian Kelly is long BTC=, US Dollar, ZBH5, HYG puts, TWTR call spreads and BBRY call spreads. He is short EWA, EWG, EWQ, EWZ, EWH, EWW, HGH5, Yen, Australian dollar, British pound, Canadian dollar, yuan and copper.

Dan Nathan

Dan Nathan is long AAPL Feb 117/107 put spreads, UAL Feb put spread, TWTR, BBRY June call spread, XLU March 48 / 44 put spread, QQQ Feb 101/ 95 put spread, XRT March 90/85 put spread and YUM Feb 72.50 puts. Today, he closed BABA Feb / Mar 95 put spread. Today, he opened YUM Feb 72.50 puts.

Steve Grasso

Steve Grasso is long AAPL, BA, CLVS, EVGN, FB, GDX, GOOGL, IMMR, KBH, KDUS, MHY, MJNA, NVIV, PFE, POT, SO, T, TMUS, TWTR and YHOO. His firm is long AXP, AMZN, TBT and MCD. His kids are long EFG, EFA, EWJ, IJR and SPY.