Ramires and Cesc Fabregas got on the scoresheet in the second half after Zoltan Gera broke the deadlock, but Jose Mourinho was left with plenty to ponder just over a week away from their first Premier League fixture of the new campaign.
In a game being played to celebrate the opening of the impressive Groupama Arena, Mourinho named a strong starting line-up for his side's penultimate pre-season friendly, with Drogba partnered with Fernando Torres up front.
There was room for two youngsters, as teenage defenders Andreas Christensen and Kurt Zouma featured alongside close-season signing Filipe Luis and Cesar Azpilicueta in the rearguard ahead of Petr Cech, but the midfield was packed with proven performers, including World Cup winner Andre Schurrle.
The vociferous home crowd were on their feet when Attila Busai sneaked in at the far post early on, but he was ruled offside before firing over the bar, while at the other end, Drogba and Schurrle forced saves from Denes Dibusz.
It was the locals making all the noise again after 17 minutes, though, when former West Brom and Fulham midfielder Gera finished off a fine cross from the right with a clinical close-range volley that gave Cech no chance.
Drogba then had to receive treatment after falling awkwardly when challenging for a high ball into the box and the striker's night was over when he worryingly hobbled off after 27 minutes, to be replaced by Oscar.
Zouma did well to head clear another dangerous cross in from the right wing, while Schurrle was narrowly wide with a free-kick for Chelsea after Willian had been clumsily felled on the edge of the area, but Ferencvaros remained 1-0 in front at the break.
Branislav Ivanovic, Gary Cahill, Mohamed Salah, Fabregas and Diego Costa came on for the visitors at half-time, but Ferencvaros started the second period brightly and should have doubled their advantage when a cut-back from the right went through two totally unmarked attackers six yards out.
Chelsea made the hosts pay for that error after 51 minutes when Ramires fired in a thundering shot from the edge of the area that flew over the outstretched arm of Dibusz and into the top corner of the net.
Cahill then had a header saved from a Fabregas corner and Oscar was only denied by a last-ditch tackle after dribbling through the Ferencvaros defence as Chelsea upped the tempo.
There was another near-miss when Cahill headed against the inside of the post and Ivanovic just failed to get to the rebound, while substitute Eden Hazard almost set up Oscar.
The winner finally came with nine minutes remaining when Fabregas dribbled past two defenders and coolly slotted home.
Fabregas had a chance to add another, but glanced his close-range header wide after great work from Victor Moses down the right and Costa missed another gilt-edged opening when shooting wide with just the keeper to beat.
Chelsea will complete their preparations for next Monday's Premier League trip to Burnley by hosting Real Sociedad on Tuesday night.
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