Nabil El Zhar had fired the hosts into a shock lead midway through the first-half.
However, after an unfortunate Juanfran own goal had levelled matters just after half-time, Tello then sped onto Messi's through ball to fire home on the hour mark.
The two combined once more 10 minutes from time and another lovely Messi pass allowed the 22-year-old to volley home his hat-trick five minutes later to leave the second-leg at the Camp Nou next Wednesday a formality.
And Barça boss Gerardo Martino hailed his side's patience as they all but killed the tie off in the second-half after a difficult opening period.
"In the first-half I was worried, but I also expect that in these type of games we will find more spaces in the second-half," he said.
"The opponent in front of us was making a huge effort and what I want is Barcelona to keep circulating the ball to make the other team tire.
"Thanks to that we found spaces in the second-half and Leo has taken advantage of them very well."
However, just as at the weekend, it start positively for the visitors as Levante took the lead from a set-piece when El Zhar prodded home from close range after Jose Manuel Pinto had parried his first effort.
Barça were handed a huge slice of luck to equalise eight minutes after half-time when Loukas Vyntra fired the ball off teammate Juanfran and the ball rebounded past the helpless Javi Jimenez into the net.
Thereafter, though, it was a procession as Tello thundered home his first moments later from Messi's first assist.
The winger then curled home his second of the evening after the defence had again been attracted towards Messi.
Tello sealed a memorable evening five minutes later with a another thumping finish from Messi's clipped ball over the top.
And Martino hinted that with Neymar sidelined, Tello's calm finishing would be rewarded with more game time in the coming weeks.
"Some players get the chance to show what they can do in 90 minutes and some only get 15 minutes.
"Until now Cristian has only been getting 15 minutes and that is very difficult.
"We will see how all the players develop in the next few weeks, but he is improving week by week. He is growing in confidence and becoming more explosive."
Barça will most likely face Real Sociedad in the last four after they beat third-tier side Racing Santander 3-1 at home in their quarter-final, first-leg.