A brace from Murphy and goals from Ando and Smith put Town top of the table
Daryl Murphy took just 18 seconds to put Blues in front and added a second midway through the half to take his goal tally to 16 for the season.
The Championship’s leading scorer could have had a hat-trick before Paul Anderson put Town in dreamland with a third on the half hour mark as Mick McCarthy’s side threatened to find the net with every attack.
Sam Saunders gave Brentford a lifeline with a goal 10 minutes from time but Tommy Smith secured the three points with a right foot beauty from just inside the box.
Saunders reduced the arrears again but his 90th minute goal was a consolation for the home side as Town stretched the unbeaten run 10 games.
Town stayed with the same side that beat Middlesbrough, Tyrone Mings not included in the 18 after being sidelined with an infected toe last week.
With leaders Bournemouth not kicking off until later, Blues got off to the perfect start with Murphy finding the bottom corner from just inside the area after Anderson released him.
Town could have extended the lead soon after, Jay Tabb, who was given a great reception by the home fans after spending the first six years of his career at Griffin Park, found space inside the Brentford box but fired over from Smith’s pass.
Town enjoyed then better of the opening exchanges and Murphy beat the Bees’ offside trap but David Button was quick off his line to avert the danger.
It took an excellent save from Button to stop Murphy grabbing a second on 17 minutes, the Republic of Ireland international spinning away from his marker and his right foot strike looked destined for the net until the Brentford ‘keeper stuck out his right hand.
Jonathan Douglas headed wide, then Cole Skuse cleared the danger as the ball cannoned back off Bart Bialkowski before Town struck again, Murphy latching on to Jonathan Parr’s pass over the top, shrugging off the defender before rounding Button to put the ball into the empty net.
Moses Odubajo was booked for upending Teddy Bishop 25 yards out, David McGoldrick fizzing a free-kick into the wall before Town made it three, Tabb crossing for Anderson to slide the ball in from close range just past the half hour.
Andre Gray forced Bialkowski into a save with his feet five minutes before the break in Brentford’s clearest chance of a first-half in which Town defended well and caused mayhem at the other end with every attacking foray into the opposition half.
It was Murphy who got the second-half underway with a bullet of a free-kick that Button held on to at the second attempt.
Bart saved well from Alan Judge’s strike as Brentford enjoyed their best spell of the game, Jota then weaving his way through Town’s defence until Parr intervened.
Noel Hunt replaced the injured Anderson on 65 minutes, the wideman taking a heavy knock that saw Tony Craig yellow carded. Brentford also changing their line-up with Nick Proschwitz and Jon Toral introduced for Douglas and Gray.
Murphy threatened to shrug off Craig again and make Brentford pay but he couldn’t get enough on his attempted chip, Blues then making a double change for the last 20 minutes with Stephen Hunt and Kevin Bru on for Tabb and Teddy Bishop.
Substitute Saunders gave Brentford hope of a grandstand finish when his right foot effort appeared to take a deflection before finding the net 10 minutes from time but Blues went up the other end and sealed the win straightaway, Smith cutting inside and curling in a right foot beauty into the top corner.
There was still time for Saunders to toe-poke the ball past Bialkowski in the 90th minute but Blues would not be denied that top spot in the Championship.
Brentford: Button. Bidwell, Craig, Dean, Douglas (Toral 65), Odubajo, Judge (Saunders 75), Gray (Proschwitz 65), Diagouraga, Pritchard, Jota. Subs not used: Bonham, Dallas, Smith, Tarkowski. Booked: Odubajo, Craig.