The winger scored his side's second goal in a nine-goal epic at the Estadio Riazor, to maintain Barcelona's unbeaten start to their league campaign.
Jordi Alba opened the scoring for the Liga leaders, before Tello's strike and a Lionel Messi goal put Vilanova's men seemingly out of sight at 3-0 up.
But, a Luiz Pizzi penalty pulled a goal back for Deportivo La Coruna on 26 minutes and an Alex Bergantinos strike 11 minutes later threatened to turn the game on its head.
Messi then grabbed his second to make it 4-2 just before the break, but the home side refused to be beaten, as Pizzi got his name on the scoresheet for a second time.
Messi completed his hat-trick with 13 minutes to go, only for an Alba own goal to set up a nervy finish, with Barca holding on to clinch a remarkable win and leave Tello a relieved man.
"We jumped into a big lead really early on, but after two good counterattacks [by Depor] we were in trouble again," he told the club's official website.
"I'm very pleased that I scored and for the confidence the manager has in me. I like to help the team and I hope I can continue doing it for years to come.
"It's always more difficult to win the three points after international breaks, but it was still three points so we can be positive about our victory."
The Catalan club are back in Champions League action on Tuesday when they face Celtic at Camp Nou.