And while Nordsjaelland did grab another goal eventually, it never really recovered as Shakhtar eased home.
Shakhtar dominated for long spells and Luiz Adriano's cool finish levelled it, before Zamora's moment of inspiration.
Shakhtar had threatened early on when Douglas Costa and Jadson tested Victor Valdes, but Barca were always superior.
In the night's other last 16 tie, Borussia Dortmund beat Shakhtar Donetsk 3-0 to progress 5-2 on aggregate.
The result leaves Shakhtar top of the standings with two wins from two, while Partizan have now lost twice.
But it wasn't all plain sailing for Shakhtar after it scored a hugely controversial goal to go to 1-1.
Gerard Pique's shot deflected in off Yaroslav Rakitskiy but Rakitskiy turned a cross in as Shakhtar pulled one back.
Toulouse are two points behind leaders Shakhtar with Bruges three points further back.
Shakhtar fans are flocking to Turkey hoping to see their side secure the first European trophy for a Ukrainian side.
Last season it was Shakhtar who won, before that it was Zenit St Petersburg, and Sevilla also won the competition.
And Shakhtar supporters are flocking to Turkey hoping to see their side secure the first European trophy for a Ukrainian side.
One of the venues is being funded by Ukraine's richest man, the football-mad billionaire Rinat Akhmetov, for his team Shakhtar Donetsk.
Jeff United defender Zeljko Milinovic was replaced with Shakhtar Donetsk's Muamer Vugdalic and Olimpija's Senad Tiganj came in instead of Cimerotic.
Holders Shakhtar Donetsk took control of Group J with a resounding 4-1 victory over an outclassed Partizan Belgrade at the Olympyiskyi Stadium.
Diego pulled one back after 31 minutes for Bremen who looked weary from their extra-time defeat to Shakhtar Donetsk on Wednesday night.
The clash pairs two of the favourites for the competition, with Sevilla pulling off a remarkable escape to go through against Shakhtar Donetsk.
BBC: SPORT | Football | Europe | Tottenham face tough Sevilla test
With a drop ball signaled by the referee, Shakhtar kicked the ball back to the Nordsjaelland goalkeeper, only for Adriano to intercept and score.
Shakhtar Donetsk, Juventus and Hamburg have all been beaten by Fulham en route to the final, with Spain's Atletico Madrid now standing in their way.
"He's not played with us or practised with the group, so I'm quite surprised he's in, " said Wenger after Arsenal's 2-1 defeat by Shakhtar Donetsk.
Arsenal will play Shakhtar Donetsk, Braga, Partizan Belgrade in Group H.
The success continues a sensational second European campaign for Fulham, who had eliminated defending champions Shakhtar Donetsk and favourites Juventus in the previous two rounds.
Chelsea offset the away loss to Shakhtar with a winner from substitute Victor Moses who scores to make it 3-2 four minutes into added time.
For Fulham and their fans, it was the perfect start as the Cottagers raced out of the blocks to stun Shakhtar and take an early lead.
Just when it looked like it would end advantage to Shakhtar, Donati fired into the far corner from a McGeady cross to set Celtic Park alight.
They have since eliminated defending champions Shakhtar Donetsk, favourites Juventus and Wolfsburg in the knockout stages, with Thursday's victory their 16th match in the competition this season.
Petersburg, Portuguese champions Porto and Ukrainian title winners Shakhtar Donetsk -- three teams who have all tasted glory in the second-tier Europa League in the last four years.
Shishatsky spokeswoman Rimma Fil told the AP that most of the passengers were likely heading for the Wednesday night Champions League football match between Ukraine's Shakhtar and Borussia Dortmund.
It left Shakhtar on top of Group E on goal difference from Chelsea, with Juventus a point adrift in third following a 4-0 win at home to Nordsjaelland .
With the job all but done, Barca played keep-ball from then on, though there was time for Shakhtar's Adriano to hit the post with a shot from a narrow angle.
As in the first leg, they had to survive some early Shakhtar pressure - but the Ukrainian side's inability to take advantage of their initial supremacy once again cost them dearly.
应用推荐