Oil entered bull-market territory this week, after quietly recovering more than 20% over the past few months. Fueling that rally is a vast improvement in market fundamentals. Oil demand, for example, has rapidly accelerated while supplies haven't expanded quite as quickly as feared, which is helping drain the glut of oil that had been sitting in storage.

While many oil stocks caught fire alongside crude and rallied sharply, several top-tier names haven't yet joined the run. Three that stand out are EOG Resources (NYSE:EOG), Halliburton (NYSE:HAL), and Core Laboratories (NYSE:CLB). Here's why this trio could quickly play catch-up, especially if market fundamentals continue getting better and push crude even higher.

An oil pump at sunset.

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This sleeping giant could soon awake

U.S. oil giant EOG Resources is one of the leaders in the shale revolution. The company built an impressive inventory of future drilling locations, currently boasting more than 7,000 that can earn a premium return of 30% after tax at $40 oil. Because those lucrative returns increase exponentially with oil prices, EOG Resources is on pace to grow its oil production by 20% this year while living within cash flow.

However, despite this impressive growth forecast, EOG's stock has fallen 5% this year. That underperformance is also coming even though EOG Resources has repeatedly blown past expectations, including reporting a gusher of production growth last quarter. Given its history of innovation and outperformance, EOG Resources will probably report another strong quarter, which, thanks to the renewed optimism in the market, might be just the catalyst the stock needs to push higher.

Worries of a significant slowdown appear to be diminishing

Oil-field services giant Halliburton has also slumped this year, with its stock falling more than 15%. Driving that decline are worries that drilling activities would dive along with crude prices. However, while Halliburton's customers showed signs that they were "tapping on the brakes," the recent rebound in crude suggests that they aren't likely to slow any further and might even start to reaccelerate.

Halliburton's North American business should therefore hold up better than investors had initially feared. While revenue probably won't continue growing by a 20%-plus rate in the near term since the rig count has fallen from its peak, margin shouldn't backtrack because it's less likely that customers will cut back much farther now that oil is heading higher. Once investors realize that, Halliburton's stock could quickly catch up to crude's rally.

Globed hands turning a valve.

Image source: Getty Images.

Getty ready for the rapid upturn

Oil reservoir specialist Core Labs has vastly underperformed the oil market, with its stock sinking nearly 19% for the year, and has even continued falling amid crude's sharp rally. That slump came even as the recovery in its financial results accelerated last quarter. Furthermore, while Core noted that lower oil prices and labor and equipment shortages would affect its third-quarter results, the company still sees revenue and earnings heading higher. Meanwhile, Core Labs continues to generate a gusher of free cash flow thanks to its capital-light business model. One of the primary usages of that capital is share repurchases, which will make an even more meaningful dent in the outstanding share count given the company's slumping stock price.

Moreover, with crude prices heading back above $50 recently, it's increasingly less likely that Core's customers will slam on the brakes. Instead, the higher prices could give them incentive to pick up the pace, since they'll have the cash flow to keep drilling, which increases the chances that Core Labs's revenue and earnings can continue climbing. While it might not quite deliver the "V-shaped" recovery in results initially anticipated, Core is getting closer to that step-change improvement.

Waiting for the wave to take hold

The oil market is slowly starting to change its tune and is flipping from pessimism to optimism because of rapidly improving oil market fundamentals. However, this bullishness hasn't fully taken hold just yet, which is providing investors with an opportunity to buy some top-tier oil stocks that still seem to have room to run. While crude could change on a dime, as it has done twice this year, the rapid rebalancing of the oil market seems to suggest that the bulls might be here to stay for a while.

Matthew DiLallo owns shares of Core Laboratories. The Motley Fool recommends Core Laboratories. The Motley Fool has a disclosure policy.