Mount's slick turn and shot in the first half would have been painful enough for Porto, who were the better side for large spells of this first leg in Seville but repeatedly lacked the precision to take advantage.
Chelsea punish wasteful Porto to put one foot in Champions League semis
A classy goal from Mason Mount on Wednesday helped Chelsea to a 2-0 first-leg win over Porto, whose wasteful finishing could have scuppered their hopes of springing another Champions League upset in the quarter-finals.
Instead, their misery was compounded by Ben Chilwell capitalising on a mistake at the back to score a late second that gave Chelsea another away goal and leaves them on the brink of the semi-finals.
They were away goals only in name given both these teams were playing in the unfamiliar Ramon Sanchez Pizjuan, where they will meet again next week, just with the home and away roles reversed.
Porto were in the home dug-out, wore their home kit, had a large club banner in the empty stand behind one goal and their anthem was the one that played out before kick-off.
And Chelsea played the part too, delivering a classic away performance of soaking up the pressure and hitting their opponents on the counter-attack, their quality in the final third proving decisive.
Real Madrid could lie in wait for the victors, after they beat Liverpool 3-1 on Tuesday.
Chelsea's win also goes some way to easing the shock of Saturday's 5-2 loss at home to West Brom in the Premier League, which ended Thomas Tuchel's 14-match unbeaten start as coach.
Tuchel decided Thiago Silva's 29 minutes before being sent off in that game were not enough to hone his sharpness, meaning Andreas Christensen was picked in the back three.
And Antonio Rudiger also returned, despite his training ground scuffle with Kepa Arrizabalaga on Sunday, which Tuchel described as a "serious situation".
Porto were regarded as the plum draw in the last eight, despite seeing off Cristiano Ronaldo and Juventus in the last 16, their task made harder this time by the suspensions of Mehdi Taremi and top scorer Sergio Oliveira.
But they were the aggressors from the outset, with Chelsea surrendering the ball and the chances.
Porto had six shots to Chelsea's one before half-time, with Mateus Uribe grazing the top of the net with an early volley and the excellent Otavio almost catching Edouard Mendy out with a corner before Zaidu Sanusi smashed over the rebound.
Chelsea, though, showed them what ruthlessness looked like when Jorginho fired a pass into Mount on the edge of the area inside the right channel. Mount took it on his back foot and twisted away from the sliding Zaidu, before firing a cool finish into the far corner.
Porto kept coming in the second half and kept missing too. Moussa Marega snuck in but his shot was saved by the feet of Mendy before Jesus Corona feathered Luis Diaz through but he took too long. Diaz curled wide after a good run by Wilson Manafa.
Chelsea absorbed them and then hit them with a sucker-punch, Mateo Kovacic's ball over the top miscontrolled by Corona, allowing Chilwell to steam clear, round the goalkeeper and finish.
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