An own goal from Mark Ellis and a backheel from Tom Eastman gave the U's a 2-0 lead at the break, a lead that never lasted long.
Sub Tyrone Barnett got one back within a minute of the restart and then levelled things up with only fifty eight minutes played.
The Shrews' other half time sub Sulley Kaikai then got two goals as well, making it a miserable second half for the U's.
There wasn’t too much in the way of penalty area action in the first twenty minutes, the only two involving Marvin Sordell.
First, he couldn’t wriggle his way through a packed Shrews’ defence and then he couldn’t make a meaningful contact at the near post from a Gavin Massey cross.
In the home side’s first attack of the half, Tom Eastman was on hand to hook clear under pressure but it hadn’t been a busy afternoon so far for the U’s defence.
Twice in the next ten minutes, the U’s had the ball in the net but both were chalked off due to offside decisions.
Massey and Sordell were the unlucky forwards to be denied by the flag but the first half hour had certainly belonged to the visiting team.
In the thirty fourth minute, a rare home attack led to Collins hitting a weak shot straight at Jamie Jones and it wasn’t a great surprise when the U’s went ahead a minute later.
George Moncur found Gavin Massey free on the right and the winger looked up to see Sordell in the middle.
His low cross was too near to Mark Ellis but the home defender got his clearance all wrong and the ball flew past Jayson Leutwiler in the home goal.
And the U’s second goal, just three minutes later, also came from an unlikely source.
Callum Harriott’s corner was whipped into a dangerous area, Frankie Kent kept it in the danger area and it fell to his fellow centre half Tom Eastman.
With his back to goal, Eastman decided his only option was a backheel, which left Leutwiler helpless once again.
A two goal lead was no more than the U’s deserved and if anyone was going to add to the scoreline, it would be the away side.
Harriott came closest, but he couldn’t keep his right foot shot under the bar after cutting inside from the left wing.
The half time whistle went with the U’s deservedly two goals to the good and there was nothing to suggest that the home side could or would get back into the game.
Micky Mellon made two substitutions at the break, and it made immediate differences to his side.
Within a minute, Tyrone Barnett gave the Shrews hope as he rose above George Elokobi at the far post to head past Jones to make it 2-1.
Ian Black was pulling the strings in the home midfield and on fifty seven minutes, he shot wide from distance after making space for himself.
He then provided the ammunition for Barnett’s second a minute later.
A left foot cross just evaded the head of Kent and Barnett calmly controlled and guided his shot past Jones to level things up.
The hosts then hit the crossbar through debutant Dom Smith, before the hosts’ other sub Sulley Kaikai had a volley blocked at the far post.
Kaikai wasn’t to be denied, and he made an excellent run to get onto the end of a through ball from Larnell Cole and round Jones to put his side ahead.
On seventy four minutes, Alex Gilbey and Macauley Bonne replaced Joe Edwards and George Moncur as the U’s were now the ones chasing the game.
Gilbey was into the action straight away and shot straight at Leutwiler, although it looked like he could have hit a first time shot rather than having a touch first.
Games can change in the space of seconds and that was the case on seventy nine minutes, with Eastman having a header superbly saved before the hosts scored a fourth.
Gavin Massey got onto the rebound from Eastman’s header but found the side netting, giving the Shrews a goal kick.
The goal kick found its way to another Shrewsbury sub, Liam Lawrence, and his through ball was volleyed home from an acute angle by Kaikai.
In the closing minutes, Sordell and Harriott had efforts at goal, but missed the target and found the keeper respectively.
The final whistle went after four minutes of added time, and it can certainly be labelled as one of the most apt examples of a ‘game of two halves’.