No-one could say it wasn't deserved, for Torquay dominated from the first whistle and only the acrobatics of 18-year-old Shrewsbury keeper Joe Hart stopped them winning by a much bigger margin.
Torquay had a flying start when the livewire Connell scored for the second time in successive games, curling a 25-yard left-foot shot in off the bar.
The clock had been running only 75 seconds.
Hart denied Connell, Jo Kuffour twice and Leon Constantine before half time but Shrewsbury still equalised in the 28th minute.
Kevin Sharp's cross skimmed off the head of defender Steve Woods for Kelvin Langmead to score with a right-foot volley from eight yards.
It would have been a travesty if Torquay had not led by half time and just before the interval they regained the lead.
French winger Mamadou Sow, who had set up Connell's opener, laid on an inviting pass for midfielder Garner to hammer the ball home from 12 yards.
Torquay seldom looked like giving up their lead in the second half.
Keeper Andy Marriott did have to scramble across his goal to tip another Langmead effort over but Hart was much the busier.
In the 53rd minute he just managed to block a fierce Connell header on his line.
And in the 62nd minute he back-peddled to take off and tip over a 40-yard volley by busy left winger Kuffour.
Shrewsbury manager Gary Peters threw on all three substitutes to try and salvage something from the wreckage and for their final stoppage time corner even Hart went up to have a go and met the flag kick but headed wide.