The 27-year-old, who faces an uncertain future at Villa Park, fired home with 25 minutes remaining after being set up by record £22million signing Wesley.
Callum O’Hare went close to doubling the visitors advantage only to be denied by a brilliant Ethan Ebanks-Landell challenge.
The latter came closest to scoring for the hosts when he headed over from close range late in the first half.
Villa rode their luck at times against a Shrewsbury team who will feel unfortunate not to have scored at least once.
But visiting keeper Jed Steer, the only Villa player to complete 90 minutes, was not forced into a save of note as the home side struggled to find their shooting boots.
Shrewsbury keeper Max O’Leary, by contrast, saved impressively from Keinan Davis in the first half, before then denying Rushian Hepburn-Murphy after the break before Hogan broke the deadlock.
Just as he had done in Villa’s first friendly of pre-season in Minnesota, Dean Smith named a different starting XI for each half.
The opening period allowed supporters to get a first glimpse of new boys Jota, Ezri Konsa and Frederic Guilbert.
It was the latter who experienced a particularly unsteady start, first being robbed by McCormick on the wing and then, moments later, outmuscled by Aaron Pierre, with the Shrewsbury full-back sending a low cross into the box which Tyrone Mings cleared.
Villa goalkeeper Jed Steer was called into his first action of the game soon after, getting down low to his left to palm away a free-kick struck well by the lively McCormick.
The hosts bright start continued when Pierre hooked a volley only a foot or so over the bar after Villa had failed to clear a free-kick.
Yet it was far from one-way traffic and the visitors, with John McGinn and Jota as driving forces, began to carve out several openings of their own.
Andre Green sent a shot into the arms of O’Leary from distance, before Ethan Ebanks-Landell was in the right place to deflect a goalbound Keinan Davis header over the bar after a quickly taken corner.
Pierre was similarly well placed to save the home side when Villa almost took the lead in comical circumstances.
A close range Jota volley, heading wide, was redirected toward goal by Romain Vincelot’s midriff with Pierre hacking clear before it crossed the line.
O’Leary, who had put in a fine display when playing for Bristol City at Villa Park back in April, then brilliantly denied Davis with a one-handed stop, tipping the striker’s close range drive over the bar after a driving run from Jota had put the home side on the back foot.
Having started the half well, Shrewsbury then finished it strongly.
Okenabirhie perhaps should have done better with a Donald Love cross which he was only able to send over the bar.
A minute later, Ebanks-Landell really should have scored after arriving to meet a McCormick corner at the far post. But from five yards out, he placed the header over the bar.
Ricketts did not make any half-time changes, while Villa sent out an entirely different outfield team, including new £22million record signing Wesley.
O’Leary, 22, made his second top stop of the afternoon with a fine one-on-one save to deny Rushian Hepburn-Murphy as the visitors started the second period brightly.
Villa appealed to referee John Brooks for a spot-kick before the hour as Callum O’Hare went down under a dangled foot but the calls were waved away.
The hosts made their first change as Shaun Whalley replaced Okenabirhie, who had taken a little knock.
Town’s longest-serving player Whalley typically livened things up. He was inches from winning a penalty on the Villa penalty box line before rounding keeper Steer outside the box and being brought down, the keeper receiving a caution.
Rather out of nowhere the visitors edged ahead with 25 minutes left. A long goal kick dropped for Wesley and the Brazillian helped a lovely ball over to Hogan who kept his composure and finished cooly.
Brilliant defending from Ebanks-Landell, not for the first time, denied Villa a second after Wesley had rounded O’Leary and teed up O’Hare in the box.
Ricketts was happy for all of his Shrewsbury starting XI bar Okenabirhie to play for most of the match with the trip to Cheltenham on Tuesday night in mind.
Meadow debutant Love blasted miles over from distance before Hepburn-Murphy shot wildly off target for the visitors.
Ricketts sent Omar Beckles and former AFC Telford man Udoh on for a 10 minute run-out before more changes even later.
The number of changes slowed the game down as a contest. Conor Hourihane sent a well-struck free-kick a foot or so wide.
Villa first half (4-3-3): Steer, Guilbert, Konsa, Mings, Taylor, Bjarnason, Grealish (C), McGinn, Jota, Green, Davis
Villa second half: Steer, Bree, Chester, Hause, Targett, Hourihane, O’Hare, Lansbury, El Ghazi, Hogan, Wesley.