Something interesting happened to Apple’s share price at about 3:45 p.m. Thursday, just as the bottom was falling out of the rest of the market — leaving the Dow down 679 points (7.3%) for the day.

That’s when Apple AAPL reversed course and started moving up.

The trend continued early Friday morning. Even as the Dow fell another 600 points in first few minutes of trading, Apple was enjoying its own private rally. In mid-morning trading, Apple was up nearly 8 points (9%) while the Dow was still deep in the red.

It closed the day at 96.8, up 8.06 (9%), while the Dow ended down 128 points (-1.5%).

The divergence is even clearer when you compare Apple’s performance with the NASDAQ (see chart.) There’s no telling how long this will last, but for the moment, Apple’s shares seem to be going their own way.

Why is this happening now? There was nothing in Friday’s analysts’ reports to explain it; indeed, Oppenheimer & Co. chose Friday morning to lower its target for Apple, to $145 from $213. And for now, none of the other four horsemen of technology — Google GOOG , Amazon AMZN and RIM RIMM — are following Apple’s lead. (See Market free fall: How Apple fared.)

What’s more likely is that Apple may have finally hit some kind of bottom — around $86 a share, a 20-month low — focusing investor attention on what’s coming in the weeks ahead: 1) a new line of high-margin notebook computers scheduled to be unveiled Oct. 14 and 2) a quarterly earnings report on Oct. 21 that are widely expected to blow past Apple’s guidance numbers.

Given the volatility of this stock, however, the trend is unlikely to last for long. The next bit of bad news for Apple is likely to come directly from CFO Peter Oppenheimer (no relation) in the company’s Oct. 21 conference call. Given the level of consumer confidence going into the holiday selling season, Apple’s Q1 guidance — always conservative — is sure to be even more chilling than usual.