However, the home side were back on level terms 11 minutes later when Cronin crossed for former England international Lee Sharpe to thump in the equaliser from just inside the box.
Sharpe was denied a second when Tigers keeper Matt Glennon pulled off a great diving save, while James Coppinger hit the bar as the Grecians piled on the pressure.
Stuart Elliott had earlier gone into the book for a dive when he went down from a Curran challenge, but there was more in it than the referee thought and Elliott limped off to be replaced by Simon Johnson in the 26th minute.
10 minutes before half time Ian Ashbee for City and Martin Thomas for Exeter both went into the book after a reaction on Ashbee's foul on Justin Walker.
However, that was the least of Jan Molby's problems as he saw goalscorer Stuart Green being given his marching orders in the closing stages of the half for striking Walker.
Things then went from bad to worse as Steve Flack put Exeter ahead in first half stoppage time from Walker's cross.
City made a double substitution at half time with Whittle and Williams replacing Strong and Dudfield as Molby re-organised after going down to ten men - something he's had a lot of practice of doing recently - but his plans struck another blow when Exeter made it 3-1 in the first minute of the second half. A cross came in and with his first contribution since coming on, Justin Whittle headed into his own net.
Gary Alexander had a chance to pull one back for City and get a goal against his former team, but headed over from Williams' cross.
That was a rare City chance as it continued to be all Exeter in the second half, and Coppinger hit the woodwork for the second time in the 56th minute.
It was an uphill struggle for City to get back into the match, and Exeter were happy to play out the 3-1 win.
Jan Molby was not a happy man after seeing his side losing out after going down to ten men, and spoke of the red card decision: "We were level at 1-1 and just starting to come back into the game. As far as I could see Stuart was using his arms to jump which is fairly normal and I'd like to view it on video to check whether or not the officials got it right.
"Exeter are a good side with some excellent players but I do believe that if we'd have had our full compliment for the 90 minutes then the result would have been different."
Meanwhile he said that there is "no excuse" for his players taking out their frustration by lashing out and getting sent off.
City line-up (4-3-3): Glennon; Regan, Anderson, Strong (Whittle), Smith; Green, Ashbee, Price; Dudfield (Williams), Alexander, Elliott (Johnson).
Un-used subs: Musselwhite, Bradshaw.
