Granted, it's an on-again, off-again relationship between stock prices and rates, but it's been "on" for the past few days. Today was no exception. Stocks were close enough to their recent, relative abyss that any further weakness would have broken key technical floors. The resulting selling would have likely helped bonds continue to rally.
Instead, stocks bounced. They didn't bounce in grand fashion (i.e. there weren't huge gains), but they were very clear about not moving any lower from yesterday's 2pm ET levels. That was basically it as far as the bond rally was concerned. Yields moved off their lows late yesterday and were jolted slightly higher by a weaker open in the European bond market.
Throughout the domestic session, there was a strong directional correlation between stocks and bonds. In other words, they were almost always moving in the same direction, even if the magnitude varied. In general, bonds sold-off steadily as long as stocks were holding steady (or better). The selling brought 10yr yields close to the 2.79-2.80% technical level by the end of the day, but those ceilings remain intact for now. The counterpoint is that the stock rally never really got extreme, so it remains to be seen how bonds would respond if stocks make it back above yesterday morning's highs.