Opening down some 300 Dow points, the stock market tried valiantly to rally for most of Monday before succumbing to an end-of-the-day rout. That the market was headed lower was no great surprise to anyone who followed the tumultuous events of this past weekend. And for anyone who was watching football instead, there was yesterday’s headline in The Wall Street Journal: “Crisis on Wall Street as Lehman Totters, Merrill Is Sold, AIG Seeks to Raise Cash.”

That’s easily the most explosive headline I’ve ever read since subscribing to the Journal. And that covers some pretty turbulent ground, dating back to the early 1980s.

Of course, the WSJ is now the property of media mogul Rupert Murdoch, who’s well known for his ability to attract eyeballs. But there’s also no denying that the failure of Lehman Brothers (NYSE: LEH)–and the US government’s refusal to prop it up over the weekend–is a watershed event.

The question is, where do we go from here? Speaking with some of my colleagues yesterday, my initial observation was holding down losses Monday was the key to a swift end to the crisis. That didn’t happen.

After bailing out mortgage giants Fannie Mae (NYSE: FNM) and Freddie Mac (NYSE: FRE) at enormous cost, the US government appears to be saying that industry was now on its own. Rather than shell out money to keep insolvent companies running, it would now allow them to fail, and simply try to control the fallout.

Some of the provisions agreed to over the weekend by the stronger banks were directly designed to do that. So apparently was the purchase of Merrill Lynch (NYSE: MER) by Bank of America (NYSE: BAC), which many speculated was done at the government’s behest as well.

We’ll see over the next few days if the government’s new strategy works. Basically, they’re betting that the market will be able to absorb the failure of Lehman without a total meltdown, either on Wall Street or throughout the financial system.

For now, however, investors are clearly spooked. The problem is other financial institutions now look highly precarious. First in line is American International Group (NYSE: AIG), whose shares lost more than 60 percent of their value Monday. But it’s far from the only major at risk, as today’s gut-wrenching drops in Citigroup (NYSE: C) and even Merrill’s savior Bank of America reflect.

Viewed in this light, it’s easy to see why the Dow fell more than 500 points Monday. It’s also no stretch that the Nasdaq dropped more than 80 points or why the broad-based Commodity Research Bureau Index dropped more than 3 percent. Even many bonds slipped on credit concerns, with the notable exception of US Treasuries, which rallied sharply.

What stands out most to me is just how little was spared in what was, at the end, wholly indiscriminate selling. Monday’s casualties included securities of companies that have shown little or no impact from the bear market stress tests of tight credit, high raw material costs and weak US growth. Rather, the institutions that dominate global trading were simply selling everything.

Ironically, the outperformers in my portfolios were Atlantic Power Corp (TSX: ATP-U, OTC: ATPWF) and Boralex Power Income Fund (TSX: BPT-U, OTC: BLXJF). One reason is both have faced some headwinds this year, and both have recently affirmed the security of their rather huge dividends. Stronger regulated utilities such as Duke Energy (NYSE: DUK) and Southern Company (NYSE: SO) were also green for most of the day before turning red in the market’s final rout.

Every selling wave in a bear market always feels worse than the last. And speaking for myself, Monday’s was certainly no exception. But we’ve seen this kind of climatic panic-selling before in the past 15 months. Each time, the market caught itself, and we saw at least a mild recovery before the bear market resumed.

We’ll see if and when that happens this time around. Meanwhile, two things are critical. First, keep your head. Monday’s pasting has left a number of good stocks cheaper than they were on Friday, and lot cheaper than they were just a couple of months ago. Panic-driven losses, however, have a way of reversing quickly.

The only stocks you really want to sell now are those attached to companies with noticeably weakening fundamentals. Those are what will cause the kind of blowups that are hard to come back from.

In my view, the economic stress tests behind this bear market are certain to ratchet up now with the Lehman failure, particularly when it comes to tight credit conditions. That means some companies that have made it so far may in fact start to falter.

Unfortunately, we’re not going to have hard numbers to prove the case one way or the other until third quarter earnings are announced, beginning in late October. And that’s a lifetime for a conviction-less market where the confidence of most players has (somewhat justifiably) been shaken to the roots.

Following the numbers, however, is still the only strategy that makes sense. It’s kept us out of the real blowups for the first 15 months of this bear market. And despite today’s overall market collapse, it’s keeping us in the game for an ultimate recovery. Finally, we’re still collecting our dividends. In short, I’m sticking with this approach.

Second, stay diversified and balanced with your holdings. That means avoiding the temptation to average down in falling stocks. Once there’s visibility on the ultimate damage to the financial system, this market will recover. Until then, however, I don’t see any great rush to buy anything, except as part of an incremental program of measured investment.

In other words, stick with good companies that continue to measure up to the stress tests and pay good dividends. Continue to own a mix of high quality from a range of sectors. But do so as unemotionally as possible.

We don’t know how much longer the selling will go on, or how much lower it will take even our high-quality, recession-resistant stocks. We do know it will eventually end, and that companies that stay strong throughout will lead the charge back. That’s where we want our exposure to this market. Other than that, keep your powder dry until this perfect storm eventually blows away.