Bear markets offer great opportunities to make money. The problem for many investors is that they're afraid to dip their toes in the water with stocks that are sinking.

But what if you could find stocks that have actually performed well, offer exceptional dividends, and are attractively valued? The good news is that these outliers exist. Here are three such dividend stocks to buy now that are bear market bargains.

1. AbbVie

AbbVie (ABBV -0.96%) belongs to the exclusive group of stocks known as Dividend Kings. The drugmaker has increased its dividend for 50 consecutive years. Its dividend yield stands at a hair under 4%.

Admittedly, AbbVie hasn't delivered massive gains for shareholders this year. But the biopharma stock has still managed to stay in positive territory for most of 2022. That's a noteworthy accomplishment in the current dismal market.

The stock trades at 12.2 times expected earnings -- much lower than the S&P 500's forward earnings multiple of 16.2. AbbVie's low valuation is due primarily to investors' concerns about Humira. The company's best-selling drug loses U.S. exclusivity in 2023.

However, AbbVie already has two worthy successors to Humira on the market with Rinvoq and Skyrizi. It fully expects these two drugs will generate sales within a few years that are greater than Humira's peak sales. AbbVie also has other solid growth drivers in its lineup, including blood cancer drug Venclexta and antipsychotic Vraylar.

2. Bristol Myers Squibb

Bristol Myers Squibb (BMY -1.42%) is another big drugmaker with a solid dividend. Its dividend yield tops 3%. The company has increased its dividend for 13 consecutive years.

Sure, that track record isn't as impressive as AbbVie's. But BMS is beating AbbVie (and most other stocks) on another important front: Its share price has soared nearly 15% year to date while the major indexes plunged.

BMS is also even more of a bargain than AbbVie is. Its shares currently trade at 8.7 times expected earnings. Like its big pharma rival, though, BMS must deal with a patent cliff. Blockbuster drugs Revlimid and Pomalyst have already lost exclusivity. The key patents for several of the company's other top-selling drugs expire in a few years. 

Don't count BMS out, though. The company could have another multibillion-dollar drug in the making with combination immunotherapy Opdualag. BMS also has several rising stars in its product lineup along with a promising pipeline.

3. Chevron

Many income investors have been fans of Chevron (CVX -1.45%) for years. That's still the case, with the oil and gas giant offering a dividend yield of more than 3.9%. Chevron is also a Dividend Aristocrat that has increased its dividend for 35 consecutive years. 

It isn't just income investors that have liked Chevron this year, though. The stock has been a big winner, soaring more than 20% year to date after skyrocketing 39% in 2021. Russia's invasion of Ukraine disrupted global energy markets and directly benefited Chevron.

You might think after Chevron's big gains that the stock would be expensive. Nope. Its shares trade at only 9.2 times expected earnings. Although this multiple is a little higher than the energy sector average of 8.1, Chevron is much stronger financially than most other energy companies.

Chevron should be able to continue paying its attractive dividend and buying back shares even if oil prices fall significantly. The company is also focusing on low-carbon projects that could pave the way for future growth. Like AbbVie and Bristol Myers Squibb, Chevron is a bear market bargain that could also continue beating the market.