The former Sunderland and Norwich striker, 24, equalised in the 50th minute to cancel out a first-half opener from Sky Blues midfielder Sammy Clingan.
Neil Mellor put Alan Irvine's men 2-1 ahead in the 55th minute and Brown added his second in the 68th minute to take his season tally to six.
Clinton Morrison grabbed a last-minute consolation for Coventry but Preston held on to return to winning ways after their 3-1 defeat at Scunthorpe on Tuesday.
The Glanford Park reverse was their first loss of the campaign and Irvine got an immediate response from his players as they reignited their promotion bid in style.
Yet it was the Sky Blues who began the brighter as Leon Best
collected possession in the fifth minute and thrashed a 25-yard shot narrowly wide.
In the 19th minute, Coventry forged ahead thanks to an excellent free-kick from Clingan.
On-loan Wolves centre-back Neill Collins, preferred to Youl Mawene in the heart of the North End defence, fouled Jack Cork 35 yards from goal.
Clingan stepped up to curl a delightful right-footed shot into the top corner to give the visitors a platform on which to build.
The response from Preston was almost immediate as Ross Wallace flighted in an inswinging corner from the left flank, only for Brown to head wastefully wide from 12 yards.
Preston continued to probe and in the 26th minute Mellor rifled a shot wide from 20 yards.
Moments later, Coventry came desperately close to doubling their advantage as Best again proved the threat.
His right-foot shot from 12 yards was superbly tipped around the post by North End goalkeeper Andy Lonergan.
The impressive Lonergan denied Best again soon after but Preston had a great chance to draw level before the break.
Richard Chaplow crossed dangerously but Brown again missed the target when he should have done better.
Five minutes after the restart, Brown rediscovered his touch in front of goal when Chris Sedgwick crossed from the right flank and Brown fired home right-footed from 12 yards.
Five minutes later, strike partner Mellor got in on the act when he ruthlessly dispatched Billy Jones' low right-wing cross.
The goals put Preston in control and Mellor tried his luck from distance from 25 yards with a strike that flew over the crossbar.
Any hopes Coventry had of salvaging a point were ended in the 68th minute when Chaplow crossed from the right flank and Brown buried another right-foot shot from six yards.
Coventry refused to give up and Lonergan denied Best again in the 82nd minute, before Morrison struck with the last kick of the game with a right-foot volley from six yards.