The Bees' summer signing struck twice in nine second-half minutes to seal the points before leaving the field with what looked like a shoulder injury.
His first came less than a minute after half time when he ghosted in between defender and keeper to poke home Bryan Mbeumo's right wing cross after a slip by defender Ryan Giles.
And the big striker grabbed his fifth in as many games less than 10 minutes later when he headed home Emiliano Marcondes' precision cross at the far post to leave City with a mountain to climb.
Toney always looked lively and was the first to test City's resolve with a neat shot on the turn from the edge of the area inside the first minute, which Marko Marosi saved.
They almost broke the deadlock on 10 minutes when Canos' first-time cross from the left was met by Marcondes, whose looping header found the roof of the net.
Coventry, without suspended playmaker Gus Hamer, looked shell-shocked for the opening 20 minutes as they struggled to find a foothold in the game.
Brentford were passing and moving the Championship newcomers off the park, without really creating anything clear-cut in front of goal.
Toney asked questions again midway through the half with a blistering half-volley brilliantly tipped wide by Marosi at full stretch.
Coventry's first attempt on target came on 38 minutes, Michael Rose arriving late and unmarked at the far post to meet Giles' free kick only to slice wide.
Mark Robins' side began to grow in confidence as the first half wore on, their well-drilled back five reducing the Bees to speculative long-range efforts.
But the disastrous start to the second spell left them powerless as Brentford turned the screw and contained their lively visitors to see out the game.
And Godden reminded the Londoners it was far from over minutes later when his instinctive near post effort was gathered safely by Raya.
Brentford managed the game well in the dying minutes, but it took a point blank Raya stop from Godden's header late on to keep the clean sheet intact.
And Ben Sheaf might have done better with an injury-time effort on goal when the ball sat up nicely but he fired straight at Raya.
Godden, a bright spark for the Sky Blues, refused to give up the ghost and fired in a low drive which again found only the gloves of the Spanish goalkeeper.
But in the end it was a comfortable afternoon's work for the Bees, who proved there is life after Said Benrahma following his departure to West Ham.