The turning point of the tie arrived nine minutes into the second half as Lionel Messi was sent sprawling inside the box by Demichelis and dusted himself down to convert from the penalty spot, before Daniel Alves added what could be a crucial second for the Catalan giants in the final minute of the 90.
City had held their own until being reduced to 10 men, with opportunities of note in short supply as both sides looked to keep things tight with a return date at the Nou Camp in the back of their mind.
Manuel Pellegrini's hosts were able to soak up plenty of pressure in the opening 45 minutes, as Barca's tiki-taka approach saw them dominate possession, but Joe Hart was rarely troubled and it was Victor Valdes in the opposing goal who endured the more nervy moments.
It only takes a matter of seconds for Barca to carve opponents open, though, and they did just that early in the second period.
With City caught napping, Messi was sprung into space and while Demichelis appeared to lunge into a challenge just outside the box, contact was made inside and he was sent trudging from the field as Barcelona's Argentine talisman sent Hart the wrong way from 12 yards out.
The visitors kept on pressing from that point, looking to make their numerical advantage count, and in the dying seconds the energetic Alves exchanged passes with fellow Brazilian Neymar before rolling through the legs of Hart.
Barcelona coach Gerard Martino had said prior to the contest that the key to victory was possession and so it proved, as the visitors controlled the ball for long spells.
Yet City appeared to have been expecting that having packed midfield.
After 14 minutes largely on the back foot, but with Barca yet to create a clear-cut chance, Vincent Kompany picked out Alvaro Negredo with a long ball.
The powerful forward controlled well on the edge of the box but Javier Mascherano managed to clear his lines.
Barca had another scare as Valdes was beaten in the air by Kompany at a corner but he scrambled back to gather on the line.
All these chances punctuated spells of prolonged Barca possession and the Catalans did eventually pierce the hard-working back line of Kompany and Demichelis.
Cesc Fabregas played in Andres Iniesta only for Yaya Toure to get back and Messi linked well with Xavi and Iniesta before shooting over.
Negredo had another chance to open the scoring before half-time but glanced a header wide from Navas' cross.
City were to rue those missed chances as Barcelona upped the tempo for the second half.
Messi was clearly in the mood and had the hosts, and particularly Demichelis, in trouble as he burst through on goal.
Demichelis could not keep pace and slid in in a desperate attempt to tackle, but succeeded only in tripping his fellow Argentine.
Contact appeared to be just outside the area but referee Jonas Eriksson pointed to the spot and gave Demichelis his marching orders.
Messi calmly stroked home the penalty down the centre as Hart dived to left.
Pellegrini sent on Joleon Lescott to reinforce the defence but recognised damage limitation was not an option and also introduced Samir Nasri.
Barca could have taken even greater command of the tie as Xavi shot over and Alves fired across goal.
City broke again but Gael Clichy wasted an opening and a well-struck Silva volley was clutched by Valdes.
The hosts, however, may have had a stroke of luck as Gerard Pique had a late goal ruled out for a marginal offside.
Edin Dzeko had a late chance for City but was harshly penalised for a foul.
There was no reprieve for City in the final minute as Alves got behind the defence and fired past Hart.