The youngster's first league goal secured a first home win since December for Colin Todd's under-pressure side and could prove the perfect tonic after a dispiriting run.
After their dismal home defeat to Oldham on Saturday, Todd rang the changes in a bid to pep up his lacklustre outfit, but there was little sign of improvement in a scrappy first half.
Blackpool skipper Peter Clarke should have done better with a free header from eight yards in their first attack and the home fans' frustration increased when striker Danny Cadamarteri completely miscued his shot from the edge of the box.
Todd's call for more fight from his players seemed to have fallen on deaf ears as they struggled to put any pressure on the Seasiders defence and City had to thank keeper Donovan Ricketts for the fact that they went in a half-time on level terms.
Six minutes before the break the Jamaican international got down smartly at his near post to push away a volley from Keigan Parker and, from the resulting corner, Ricketts again had to stretch to a deflected shot from the same man on to his crossbar.
With the news of other relegation rivals winning Todd brought on youngsters Brown and Joe Colbeck, but it was midfielder Lewis Emanuel who posed the biggest threat.
Having seen Blackpool keeper Lee Jones scramble his goal-bound cross round a post early in the second half, Emanuel then set up a chance for Brown with a strong run down the left but the teenager saw his difficult volley fly wide.
With five minutes to go another Emanuel cross threatened to break the deadlock but Blackpool centre-half Marc Joseph positioned himself superbly to head the ball clear at the far post.
Blackpool midfielder John Murphy wasted a great chance to snatch three points for the visitors when he blazed over and Brown made him pay dearly.
The Blackpool defence struggled to clear the danger as City pressed forward in the dying minutes and when Colbeck flashed the ball across goal Brown threw himself at it to glance his header past the stranded Jones.