Wenyeji hao walipewa penati iliyozua utata kufatia Casemiro kudaiwa kumfanyia madhambi Andre Schurrle penati ambayo ilisukumwa kambani na Ricardo Rodriguez.
Safu ya ulinzi ya Real Madrid ilikuwa dhaifu ilishuhudiwa ikimruhusu Bruno Henrique kutengeneza bao la pili lililofungwa na Max Arnold.
Madrid walijitahidi kupambana kubadili matokeo ya mchezo lakini haikuwa rahisi kufanya hivyo huku wakiwa wamebaniwa penati ya mapema.
Kichapo hicho kimekuwa ni cha kwanza kwa Real Madrid kwenye robo fainali ya Champions League tangu mwaka 2004 na kinawapa kibarua cha ziada kwenye mchezo wao wa marudiano Jumanne ijayo kwenye uwanja wa Bernabeu.
Rekodi muhimu unazopaswa kuzifahamu
Navas amefungwa kwa mara ya kwanza kwenye michuano ya Champions League baada ya kucheza kwa dakika 738 bila nyavu zake kutikiswa.
Real wamefungwa magoli 2-0 kwa mara ya kwanza kwenye mashindano ya klabu bingwa Ulaya tangu mwaka 2014 ambapo walichezea kichapo kutoka kwa Borussia Dortmund. Hiyo ilikuwa mara yao ya mwisho kupoteza mchezo kwa magoli mawili.
Wolfsburg sasa wanafanikiwa kushinda mchezo wa tano wa Champions League mfululizo.
Wamepoteza mechi moja kati ya mechi zao nane za nyumbani za Champions League, walifungwa na Manchester United kwa magoli 3-1 December 2009.
Cheki magoli ya Wolfsburg wakati ikiichapa Real Madrid
Wolfsburg star player Julian Draxler, who has previously been linked with Arsenal, takes the ball down acrobatically
Real Madrid midfielder Casemiro was unfortunate to concede a penalty for an apparent foul on Andre Schurrle
The Brazilian midfielder looks on bemused as Wolfsburg's Bruno Enrique and Schurrle celebrate being awarded a penalty
Rodriguez sends Real Madrid keeper Keylor Navas the wrong way to hand the hosts a surprise lead
Wolfsburg players celebrate Rodriguez's opening goal as Real Madrid's superstars head back to the centre circle
Wolfsburg head coach Dieter Hecking pumps his fists in excitement after seeing his side take a surprise lead
Draxler was still the star of the show and from Henrique’s lofted pass he volleyed into the side netting. An even greater mystery was why Brazilian full-back Danilo had been left alone to deal with the German.
Madrid finished the half strongly with Toni Kroos testing Benaglio but Benzema’s knee never made it to half time and Jese had to come on. It was the substitute who sent Bale bursting down the left at the start of the second half but when he crossed for Ronaldo the Champions League’s top scorer skewed his shot wide.
He then slipped as he shot from the edge of the area. Madrid’s night was getting worse instead of better and Draxler was still a threat crossing from the left but sending his centre just beyond Henrique.
France international Karim Benzema (left) receives medical attention before being substituted in the first half
Arnold celebrates sending Wolfsburg 2-0 up after another lapse of concentration from Real Madrid's defenders
The German midfielder (centre) is congratulated by team-mates Vierinha (left) and Bruno Henrique (right)
Real Madrid manager Zidane watches from the sidelines as Rodriguez heads the ball in his vicinity
Bale speeds away from Portuguese striker Vieirinha as Real Madrid chase the game from behind
Ronaldo can only smirk after seeing another opportunity for Real Madrid to get back in the game go begging
Real Madrid forward Jese Rodriguez (right), who replaced Benzema, sees his shot saved by Wolfsburg No 1 Diego Benaglio
Wolfsburg midfielder Draxler tries to get in front of Pepe to clear a Real Madrid corner in the second half
Former Chelsea winger Schurrle (right) holds off his fellow World Cup winner Toni Kroos at the Volkswagen Arena
Players from both sides clash as Real Madrid let their frustration get the better of them in the second half
Madrid's Bale and Wolfsburg goalscorer Arnold are each shown the yellow card as tempers fray in the second half
Just as Wolfsburg were looking for Draxler at every opportunity so Real Madrid were picking out Bale as often as they could and his whipped cross from the left found the head of Ronaldo but he could not beat Benaglio. He was not having his greatest night after Saturday’s winner in the Camp Nou. Ronaldo won a free-kick on the edge of the area but fired it straight into the Wolfsburg wall.
You know things are bad when Luka Modric is hooked and his number came up on 64 minutes. Casemiro was left on the pitch and his nightmare continued when he gave the ball away and only a last-ditch challenge from Sergio Ramos prevented Schürrle scoring.
Bale was booked for arguing with Arnold after he clashed with Marcelo. The Wolfsburg midfielder also went into the book, Marcelo had thrown himself down holding his face hoping for a red but the card was yellow.
Both Ronaldo and Bale tested Benaglio late-on but there was no way back into the game and Real Madrid now need to score three at the Bernabeu next Tuesday to stay in the tournament.
A fan is chased by stewards after struggling to contain his excitement by invading the pitch