Holt came close after heading a David Beresford free kick just over the bar in the 17th minute.
But it was Lawrie Dudfield who put City ahead 8 minutes later. Greaves headed across to Dudfield who hit the post. Alexander then crossed the ball back and Dudfield turned it in.
Michael Oliver equalised for Rochdale in the 32nd minute thanks to sloppy defensive work. Glennon got a hand on the header but was unable to keep it out, and 'Dale had it back to 1-1.
However, City's lead was restored just before half time, with Alexander's ball to the back post knocked in by Dudfield for his second.
But the home side equalised again 10 minutes into the second half. Justin Whittle fouled half time substitute Kevin Townson, and Simpson's free kick was met by Patrick McCourt, who himself had only been on the pitch for two minutes.
'Dale then took the lead for the first time of the game in the 64th minute, with Townson finding the net from a rebound.
There's was no way back for City, with Rochdale dominating the second half, but it was a more encouraging performance for Jan Molby with recalled forward Lawrie Dudfield finding the goal again.
City line-up (4-4-2): Glennon; Petty, Whittle, Mohan, Van Blerk; Beresford, Greaves, Sneekes (Edwards), Holt; Alexander, Dudfield (Caceres).
Un-used subs: Musselwhite, Williams, Whitmore.