The forward netted his fourth goal in as many games to secure the points and lift the Baggies back to the top of the Championship table.
In what, overall, was a match lacking in quality - both teams struggled to create clear-cut chances.
Following a drab first-half, midfielder Ivan Sunjic hit the bar for Blues.
Then after Grant's goal, Kyle Bartley saw a header from a corner well saved by Matija Sarkic.
But on a night where endeavour and grit was the main quality on display, one moment of genuine class was enough to win it with Grant ferociously finding the corner with a strike from 20-yards.
The result saw the Baggies move back to the top of the table on goal difference - with Valerien Ismael's side level on points with Bournemouth who have a game in hand.
Ismael opted to make two changes from the team that fell to defeat at Stoke when naming his starting line-up.
Having underperformed in that game, Jordan Hugill came out the side and was replaced by Matt Phillips.
That move saw Callum Robinson shift to become Albion's central striker with Phillips on the right and Karlan Grant on the left in a 3-4-3 formation.
At the back, fit-again Matt Clarke also returned to partner Sami Ajayi and Kyle Bartley at the heart of the defence.
His return allowed Conor Townsend to revert to left-wing back with Adam Reach forced to make do with a place on the bench.
Blues, who entered the game having lost four of their last five games, lined up in a 3-4-1-2 formation.
It saw Manchester United loanee Tahith Chong start in the number 10 role with Lukas Jutkiewicz partnered by Scott Hogan up front.
Former Albion target Troy Deeney was amongst the substitutes.
As is often the case in a derby, the opening 15 minutes proved scrappy with both teams preventing each other from building any rhythm.
But the game suddenly sprung into life when Townsend hit a thunderous drive from 25-yards that Matija Sarkic did well to tip over.
From the resultant corner, Blues countered brilliantly with Hogan finding Chong who charged into the box only to be stopped by a challenge from Townsend which had to be timed to perfection.
From the Blues' corner, Kristian Pederson hit a fierce drive that went through the legs of Bartley before being blocked by Ajayi.
Those chances aside, the game continued to be scrappy and uneventful as the clock ticked past the hour mark.
Robinson saw a shot inside the area blocked while Grant saw a fierce strike from 20-yards sail narrowly over.
But overall, Albion's plan to go long was playing into Birmingham's hands with their back three finding it too easy to deal with the balls being sent forward.
And it was the visitors who then created the best chance of the half just moments with Jutkiewicz producing a glancing header from a long throw that sailed narrowly wide.
Ismael made a change at the break with Hugill replacing Robinson.
Then on the hour, Jayson Molumby replaced Alex Mowatt after the former Leeds man took a knock to the foot he initially hurt at Stoke.
Overall, the Baggies continued to do very little other than huff and puff.
And they should have fallen behind when Hogan danced past Ajayi far too easily before hitting the byline and cutting the ball back to Ivan Sinjic.
Just eight yards out, the Croatian really should have made the net burst.
But instead, he side-footed a strike that clipped the top of the crossbar before sailing over.
That miss proved particularly costly when - out of nothing - Grant put Albion ahead in the 75th minute.
There really didn't seem to be a lot on when the forward collected the ball from a throw-in.
But from 20-yards he then produced a superb strike to thunder the ball into the bottom corner - with Sarkic having no chance of keeping the ball out.
Both Albion - and the game - needed that moment of quality with that match suddenly becoming much more open.
Blues almost pulled level when Clarke almost sent a header into his own net from a long throw.
At the other end, Townsend turned a brilliant Grant cross wide at the back post.
Then right at the end, Bartley rose highest to meet a corner only to see his header kept out with a brilliant stop from Sarkic.
Albion: (3-4-3) Johnstone, Ajayi, Bartley, Clarke, Furlong, Livermore, Mowatt (Molumby 61), Townsend, Phillips, Robinson (Hugill 46), Grant (Reach 90).
Subs not used: Button, Bryan, Kipre, Snodgrass.
Blues (3-4-1-2): Sarkic; Colin (Bela 47), Sanderson, Roberts, Friend (Graham 83), Pedersen; Gardner, Sunjic, Chong, Hogan, Jutkiewicz.
Substitutes: Trueman, Dean, Woods, Deeney, Aneke.