The keeper was at full stretch to deny Scott Golbourne after both teams were successful from their first five attempts, to ensure Paul Harsley’s side’s mature display was rewarded with victory.
City were comfortable for large parts of the game, but trailed to Golbourne’s 25-yard thunderbolt before Tommy Doyle levelled with an equally impressive 20-yard free-kick to take the game to the drama of penalties.
Harsley's youngsters were as cool as you like from the spot, as were the hosts, with Grimshaw producing a crucial save during the first round of sudden death kicks.
With City on the front foot and looking to dictate play and Shrewsbury sitting deep and countering quickly, this cup tie was a game of cat and mouse throughout.
A Doyle scissor-kick had Max O’Leary scrambling across his goal line as early as the fourth minute, but while Harsley’s side had most of the ball, it was the hosts who had the better of the chances early on.
Left-winger Ryan Giles was the architect of much of their best play, twice crossing for Lenell John-Lewis to head over, before forcing Grimshaw into a fine save with a 30-yard drive.
But he was powerless for the opener, as Golbourne unleashed a left-foot rocket to net his first goal in six-years.
City were undeterred and enjoyed their best spell immediately after, with Morgan Rogers firing straight at O’Leary when Nabil Touaizi had squared at the end of a lung-busting run from deep in his own half.
Doyle tested O’Leary again just before the break, with a dipping free-kick, while Grimshaw had to get his body behind a similarly struck Ollie Norburn effort as the second half restarted in the same vain.
But City had more joy in the final third as the game progressed.
Adrian Bernabe flashed a header inches over the bar from a Doyle cross, which left the skipper beating the advertising boards in frustration, but moments later he was jumping in jubilation as his free-kick curled inside the near post to level the score.
It was all City as the game reached its finale.
Keke Simmonds wriggled free of two defenders and curled one the wrong side of the post as we upped the ante, but the Shrews’ defence dealt with the host of crosses that peppered their area.
And so to penalties, where City's maturity shone through again.
Doyle, Bernabe, Simmonds and Rowan McDonald all netted comfortably, though Ian Poveda and Lewis Fiorini were relieved as O'Leary's hand wasn't strong enough to keep out their kicks.
Shrewsbury matched us like for like, so it was over to Grimshaw, who has form in shoot-outs, and he produced a superb save from Golbourne's well struck effort.
How we lined up
Harsley made six changes to the team that lost to Bolton Wanderers in our final group stage game.
Grimshaw’s goal was protected by a back four of Diounkou, McDonald, Harwood-Bellis and Ogbeta. Pozo sat deepest in midfield with Doyle and Bernabe just ahead of him.
Touaizi led the line up front with Poveda on the right and Rogers on the left.
What it means
City progress to the third round of the competition for the second consecutive season.
The draw for that stage, which remains regionalised, will take place live on Sky Sports News from 7.15pm on Thursday 5 December.
The EDS are back in action on Friday evening, when they make the long journey to Southampton for a Premier League 2 fixture that kicks off at 7pm.