The hosts took the lead within the first five minutes as a free kick over the top allowed Rudy Gestede to race on to the ball before blasting a shot into the top corner.
Brentford came close to finding the equaliser midway through the first half as Harlee Dean latched on to Jota's corner to send a dangerous header towards goal, but goalkeeper Jason Steele was able to tip it over the bar.
On the half-hour mark Rovers had a good chance to double their lead when Tom Cairney's cross from left fell to Gestede, who teed up Chris Taylor for a deflected shot that Steele struggled to hold on to.
Blackburn had the final say in the third minute of first-half stoppage time, however, as neat interplay on the edge of the visitors' box saw the ball fall to Taylor, who smashed an angled shot into the roof of the Bees' net.
The action kept flowing after the restart as Brentford equalised for the second time in the match, and it came in impressive fashion.
Jota picked the ball up inside his own half in the 52nd minute and marauded forward, with no Blackburn players coming forward to challenge him, before he took aim from 20 yards out and found the bottom corner of the net.
Rovers set about trying to get back into the lead and came close on a number of occasions through Jordan Rhodes, while Gestede sent a left-footed effort over the Bees bar in the 70th minute.
Brentford then sent their fans into a frenzy when they took the lead with just six minutes to go, Jota's deflected shot being saved by Steele but pushed into the path of Andre Gray, who bundled home from close range.
The result means that Blackburn remain 10th in the Championship table, while Brentford continue to trouble the top six.