Kenny Miller tumbled when there appeared to be little contact with Hibs defender Sol Bamba.
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From the resulting corner, Sol Bamba's header crashed into the turf and over the crossbar.
BBC: SPORT | Football | Scottish Premier | Hibernian 2-0 Aberdeen
Ma-Kalambay spilled McClenahan's shot and Bamba had to act quickly to clear the danger.
Rangers were more positive after the break and went ahead after 64 minutes thanks to Bamba's unfortunate intervention.
BBC: SPORT | Football | Scottish Cups | Dunfermline Ath 0-2 Rangers
The album includes tributes to Muslim leaders such as Sheikh Amadou Bamba, founder of Mouridism, Senegal's Muslim brotherhood.
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Ivory Coast's UN ambassador, Youssoufou Bamba, told the UN Security Council that he thought the current level of security was good.
Mr Bamba's comments echo a recommendation by UN Secretary General Ban Ki-moon.
Sasa Papac saw a long-range drive tipped wide by the keeper before Boyd blazed over after escaping the challenge of Sol Bamba.
Hibs were without Sol Bamba and Colin Nish through injury, with youngsters David Wotherspoon and Paul Hanlon both coming into the starting line-up.
Los Lobos hit it big in 1987, recording the soundtrack to La Bamba, the film starring Lou Diamond Phillips as rock star Richie Valens.
Fletcher doubled his tally and sealed the winner for Hibs with a left-footed strike in the 63rd minute, moments before Souleymane Bamba was dismissed.
In between those efforts in a breathless second half, Hibs defender Bamba strode forward unchallenged from midfield and sent a raking drive just wide.
Hibs went back on the offensive and Jones hit the post from Chris Hogg's cross with Bamba inches away from latching on to the rebound.
Murphy was booked harshly for diving by Brines midway through the half when he was brought down by a sliding challenge from Bamba inside the box.
Boyd then shrugged off Bamba and crashed in a wonderful dipping shot from 30 yards, while Hutton and Charlie Adam went close to extending the lead.
BBC: SPORT | Football | Scottish Cups | Dunfermline Ath 0-2 Rangers
When Jure Travner eventually sent in a dangerous cross, Sol Bamba was able to clear athletically from in front of his own goal under little pressure.
Moments later, new signing Bamba, who featured recently for Ivory Coast at the Olympics, was shown a red card for his second-bookable offence following a rash challenge.
Celtic replied at the other end when McGeady fed Marc-Antoine Fortune inside the Hibs penalty area, but Souleymane Bamba made the block and the Frenchman was denied.
Sol Bamba put his keeper under pressure with a poor header back towards goal, but the Hibernian number one managed to smother the danger before Sheridan could pounce.
Goodwillie tapped in his second after 35 minutes, but Sol Bamba struck from close range just before the break and Paul Hanlon turned home an Edwin de Graaf cross.
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Bamba capped a dismal night for his side when he handled the ball in the box, Craig's penalty deflecting off the unlucky Smith and into the back of the net.
They were restricted to a couple of high balls from set-pieces aimed at Sol Bamba, with the defender failing to get sufficient purchase on his headers to threaten the visitors' goal.
The Hibs manager steered clear of any controversy about the decision to award Rangers a penalty, when Sol Bamba challenged Kenny Miller, from which Kris Boyd put the home side 2-0 ahead.
Although Sol Bamba moved into midfield to make way for returning centre-half Chris Hogg, a first starting place for former Gretna playmaker Fabian Yantorno meant it was a particularly attack-minded Hibs line-up.
The Scotland striker spun off Bamba and latched on to a long hopeful pass, allowing it to bounce once then crashing a shot over Dorus De Vries from all of 30 yards.
BBC: SPORT | Football | Scottish Cups | Dunfermline Ath 0-2 Rangers
The 21-year-old winger again cut inside and shrugged off the challenges of Galbraith, Michael Hart, Bamba and Liam Miller before tucking a cool right-foot finish low past Brown from just inside the penalty box.
Mr Bamba said any adjustments to the size of the force would need to be offset "by the deployment of qualitative resources, such as surveillance drones for the border zone between Ivory Coast and Liberia".
However, Mackie almost opened the scoring in spectacular fashion with a perfectly timed scissor-kick from a Richard Foster cross after eight minutes, but Sol Bamba was in the right place to head the goalbound effort clear.
That decision was clear-cut, but Hibs strongly disputed the red card that completed Bamba's miserable day, although it looked like the defender was the last man as he tripped the rampaging Nade 25 yards from goal.
Elsewhere, Wigan's Steve Gohouri has sealed his place on the plane after missing out on Angola, while Hibernian's Sol Bamba, who scored in Les Elephants' 2-2 draw with Paraguay in France this week, is among the defenders travelling.
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