The Reds fell behind in west London to Keane Lewis-Potter's header but the game turned just before half-time when Yehor Yarmoliuk was shown a straight red card for a headbutt on Jeremy Jacquet.
Liverpool made their man advantage count as Victor Munoz levelled before Isak rifled in his fifth goal of the season on his return from injury.
But the visitors struggled to see the game out comfortably, even after Vitaly Janelt saw a second yellow card in stoppage time to reduce the Bees to nine men.
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"I think there's still lots to improve. We're taking steps and we're grabbing points on the way which is important," said Isak, who was left watching the final stages as an anxious spectator after being replaced.
"Us from the bench were screaming for the team to keep the ball and just play out the game."
Victory lifts Andoni Iraola's men into fifth in the Premier League and within two points of second-placed Arsenal.
But the Liverpool boss was also frustrated with how his side managed the game after Isak's 70th-minute winner.
"I think we played really well until the 2-1. After that we started to protect something, I think we didn't manage the last minutes well," said Iraola.
"We lacked some composure on the ball. Sometimes it was just about keeping the ball more and not going for the goal with the first chance."