An early second-half header from Nicolo Barella and Romelu Lukaku's late penalty sealed a dream first leg result for the Italian outfit, and their under-pressure manager Simone Inzaghi.
Having won none of their last six matches, Inzaghi's future at Inter looked perilous, as he was reportedly given just three games to save his job, but tonight's performance, which was dominant from start to finish, will rightfully earn him plenty of plaudits.
For Benfica, this result represents a second consecutive defeat, both of which have come at home, after Porto won here on Friday, and they will have a mountain to climb at San Siro next week.
In only the second meeting between these sides in this competition, after the 1965 final which Inter won on home soil, and the game never really got going in the first half.
Inter had some promising opportunities but failed to create any meaningful chances on the Benfica goal, with a vital interception from Morato stopping Lautaro Martinez from playing Edin Dzeko through on goal being one of the most notable moments of the half.
Everything good about Inter in the final third came through Federico Dimarco at left wing-back, as two very dangerous crosses could easily have provided a goal on another day.
Benfica seemed very lacklustre and did not threaten the Inter backline much, while the Nerazzurri were content at shutting up shop and hitting their hosts on the counter.
The Inzaghi master plan worked a treat though shortly after the break, as the visitors took the lead with their first shot on target of the evening.
A sensational cross from Alessandro Bastoni allowed one of the smallest players on the field, Barella, to ghost in and head home smartly beyond Odysseas Vlachodimos just six minutes into the second half.
Moments later though, Inter were incredibly fortunate not to be pegged back after Alejandro Grimaldo completely miskicked his effort with the goal at his mercy in the six-yard box, as the Inter rearguard were then able to scramble the ball to safety.
Inter continued to frustrate Benfica and had another excellent chance of their own, when Joaquin Correa fed Henrikh Mkhitaryan though, but the Armenian was unable to beat Vlachodimos at his near post.
As the final 10 minutes approached, it was almost deja vu as a near identical Bastoni cross this time found Denzel Dumfries who was brilliantly denied twice, first by Vlachodimos, and then on the goal-line by Morato.
However, it would be Dumfries who played a big part in the decisive moment of the match less than a minute later, when his cross was blocked by the arm of Joao Mario, and after a VAR check, referee Michael Oliver pointed to the spot.
Substitute Lukaku stepped up from 12 yards out, and despite Vlachodimos going the right way, there was too much power on the low drive by the Belgian as Inter took a 2-0 lead.
With Benfica demoralised, they were fortunate not to go 3-0 down when Dumfries found himself in an advanced position down the right once more, but Robin Gosens just could not adjust his body in time as the ball flashed along the area.
Inter continued their gameplan of restricting Benfica to very little, and they saw the game out to seal a 2-0 success on the night, with Onana called into action late on down to his left to brilliantly deny Goncalo Ramos, who had a very quiet night.
After not losing in 17 matches, Benfica have now lost back-to-back games for the first time under Roger Schmidt, and unless they can pull off a miraculous turnaround next week, they look set to lose a sixth straight Champions League quarter-final tie.
Before the return leg next midweek, Benfica can go one step closer to sealing the Primeira Liga title if they return to winning ways away to Chaves.
Inter have a crucial clash in terms of qualifying for next season's Champions League, facing Monza at home in an encounter they are fully expected to win.