Barca put six goals past the beleaguered visitors before half-time en route to their largest ever opening day success.
While they could only manage one more in the second period - when summer signing Neymar was brought on for his league debut - they had already served notice that there would be no early jitters under their new boss.
Martino was brought in to replace Tito Vilanova last month after the former coach confirmed he would stand down to continue his fight against cancer.
Any notion Barca might be sluggish following the emotion of their summer was, however, quickly dispelled as Manchester United target Cesc Fabregas put in a man-of-the-match display.
The midfielder was involved in five of the seven goals as he left it to Lionel Messi (two), Pedro (two), Alexis Sanchez, Dani Alves and Xavi to get on the scoresheet.
The champions took just three minutes to open the scoring with an incisive passing move that was a portent of things to come.
Xavi slid a first-time pass into the path of Fabregas and, with the away defence stepping up, his only decision was whether to score himself or play in Sanchez. The midfielder chose the latter, rolling a pass beyond goalkeeper Keylor Navas for Sanchez to tap in.
If Levante feared the early goal was a worrying sign, they were right.
Messi unsurprisingly got in on the act on 12 minutes, following a one-two with Fabregas, who then saw a shot blocked by Navas only for it to fall for Alves to stroke into an empty net.
It was 4-0 before the half-hour as Pedro's run was picked out by Messi and he located the far corner.
Navas tried to stem the bleeding with a couple of good saves to deny Messi and Xavi only to then see Adriano win a soft penalty on 41 minutes under the merest of contact from Pedro Lopez.
Messi tucked away the spot-kick but there was still time for a sixth before half-time, the influential Fabregas again involved as he weighted a return lob-pass perfectly for Xavi to scruffily poke in.
With the game over as a contest the second half was mostly about which Barca players could get their names on the scoresheet.
Central defender Gerard Pique twice ventured forward early on, only for the alert Navas to snuff out the danger. Adriano drew two more quick saves before the anticipated introduction of Brazil international Neymar was made on 64 minutes.
He watched on as Levante contributed to their own woes on 74 minutes when Hector Rodas woefully under-hit a free-kick back to the goalkeeper, allowing Fabregas to intercept and again unselfishly play in Pedro.
It was the last of the scoring as Victor Valdes was only called to make his first save in injury time.