In a game of peaks and troughs, a quiet opening was ended in the 24th minute through Lasse Vibe's composed finish.
The lead lasted 13 minutes thanks to Lawrence, whose cross-cum-shot evaded everybody and nestled into the bottom corner.
But even though the hosts had to settle for a point that leaves them 16th, Bowyer focused on the on-loan Leicester man's performance after his second goal of the season.
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He said: "He's a wonderful player, a joy to watch. He's one of these players that when he picks the ball up, half-turns and starts running, you get off the edge of your seat because you know something's going to happen.
"I think today in the second half, he had a couple of runs and looked like he would make something happen. He's a fabulous talent."
Blackburn have now won just one of the last six but they are unbeaten in their last three and have tasted defeat just once at home since August and Bowyer was pleased with the way his team battled in a game in which they were not at their best.
"On performance level, it's probably not the standards we've met all season really but we showed a different side to us today and we had to stick in, dig in and I thought we did that, but on performance, we've played a lot better this season for sure," he said.
"The important thing today was that we didn't get beat. Even though we haven't played at the levels we've set, we didn't get beat. We dug in and - but for that last save from David Button - we could have been talking about a fabulous end to the week."
On return to his former club, Brentford head coach Lee Carsley was pleased with the performance his players put in as the Bees extended their recent run to just one defeat in six.
He said: "I thought the first half was pretty even. We had a really good 25-30 minutes and they scored their goal which was a little bit lucky and they pushed on a bit to be fair.
"Half-time came at a good time for us where we regrouped and tried to re-focus the players on what was working in the first half, and we had some really good opportunities in the second half, maybe that final pass or choice of finish, we could have got three points.
"Having said that, Butts (David Button) has made a really good save in the second half, probably the save of the game. In that respect it's always a tough place to come. They've got some good players, some really dangerous players."
After moving up to 11th in the league and stretching their unbeaten away run to three games, Carsley explained how his team planned to keep Blackburn's star striker Jordan Rhodes quiet. The lethal marksman hardly had a sniff during the game and Carsley said his team set out to deny him space.
"We said that when the ball was wide, to grab hold of him basically because we watched the amount of crosses Blackburn put in and nine times out of 10, he's on the end of them. Obviously he's a good player, and on both sides, Blackburn got a lot of good crosses into the box," he said.
"We knew it was important to, as blunt and brutal as it sounds, just grab hold of him."
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