City had only themselves to blame for letting the game go to extra-time as they had comfortably protected their 2-0 first leg lead until the late drama.
The visitors had taken the sting out of the game during a dour first half in which Aalborg lacked any sense of urgency.
Vincent Kompany and Pablo Zabaleta were paired as defensive midfielders in front of the City back four and they helped give the visitors a rare air of solidity away from home.
If anything, City looked the more likely to score and Evans should have done so when he was played through on goal by an excellently weighted Stephen Ireland pass, but the Welshman skied his shot.
The home side eventually showed a threat on goal when a neat passing move culminated in Shelton nodding down for Caca to send a low shot just wide.
Aalborg took heart from the chance and thought some increased pressure on City should have resulted in a spot-kick after Andreas Johansson went down following a Javier Garrido challenge.
The denial of a penalty appeared to galvanise Aalborg, but they should have been put out of sight when Robinho, who had been a peripheral figure in the match, side-footed a shot against the crossbar after an Ireland pull-back.
Evans had a shot blocked by Aalborg keeper Zaza before Shelton scored to spark a late comeback.
City had let a two-goal lead slip against Aalborg's league rivals FC Copenhagen in the first leg of their tie in the last round and again succumbed under duress.
Evans was adjudged to have handled a cross and Jakobsen made no mistake with a 90th-minute spot-kick to signal extra-time and penalties.
Manchester City manager Mark Hughes: "Maybe lady luck smiled on us, maybe that's a good sign.
"You scratch your head and wonder how that situation developed, but we've made it through to the next round.
"Knowing Shay was in goal for us gave the real confidence taking their kicks. I think they had a real belief that Shay would play a hand."
AaB: Zaza, Bogelund, Lasse Nielsen, Jakobsen, Beauchamp, Due (Nomvethe 46), Johansson, Augustinussen, Caca (Kristensen 106), Risgaard (Tracy 77), Shelton. Subs Not Used: Kenneth Nielsen, Sorensen, Ronnie Nielsen, Dalsgaard.
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