With main rivals Switzerland not in action on Wednesday, Roberto Mancini's side capitalised to take a three-point lead at the top of Group C.
Sensi's 47th-minute effort put them ahead, with Immobile, who had squandered several gilt-edged chances, scoring a penalty with the final kick of the game.
Immobile's previous profligacy would have proved costly if not for Gianluigi Donnarumma, Italy's goalkeeper producing a fantastic save from Tautvydas Eliosius to set the stage for the Lazio forward to make amends from the spot late on.
Italy made it three wins from three to start their World Cup 2022 qualification campaign by seeing off Lithuania by the now familiar scoreline of 2-0.
Goals from Stefano Sensi and Ciro Immobile bookended the second half on Wednesday, as Italy took a three-point lead in Group C.
The Azzurri have won their last five matches 2-0, and are unbeaten in 25 games under Mancini, which brings him level with Marcelo Lippi's best haul – only Vittorio Pozzo (30) has managed a better such streak.
Lippi guided Italy to a 2006 World Cup success, and Mancini did not shy away from wanting to emulate one of his predecessors.
"I'm happy we are top of the group, it's pleasing, but records are standalone issues compared to real results," he told reporters.
"I hope to match Lippi at the World Cup, maybe in December 2022."
With three qualifying wins under their belt, Italy's focus will now switch to the upcoming Euros, rearranged from last year.
Mancini picked a 38-man squad for this latest round of internationals, and suggested it would be prudent for UEFA to accommodate larger squads than the usual 23 at this year's tournament.
"I think it could be a good idea to be able to name bigger squads for Euro 2020," Mancini said.
"I think it could be the right thing to do. The problem would above all be if a couple of players had problems in the tournament, as it's difficult to call them back after that, when players are on vacation."
Italy recorded 29 shots against Lithuania, with 11 of them on target – the excellent Tomas Svedkauskas pulling off nine saves.
Immobile, who scored from the spot with the last kick of the game, was particularly wasteful, sending a close-range header wide after seeing two efforts saved by Svedkauskas.
The 31-year-old Lazio forward has scored eight goals in World Cup qualifiers, the joint-third most in Italy's history – along with Daniele De Rossi – and Mancini believes fatigue played a big part in Immobile's profligate display.
"Ciro gave everything he could today," Mancini added. "The players aren't in the best shape right now, they are lacking sharpness, but the goals will come more consistently for him."
Kane netted almost immediately after coming on as a 70th-minute substitute against Lithuania at Wembley, wrapping up a 4-0 win with a thumping far-post header.
The then 21-year-old, who had already scored 29 goals for Tottenham that season, was given a standing ovation as he took to the field and it did not take him long to get the sell-out crowd back on their feet as, with one of his first touches, he found the back of the net.
Wayne Rooney, Danny Welbeck and Raheem Sterling scored England’s other goals, but the headlines belonged to Kane after a one-sided Euro 2016 qualifier.
Asked if he knew how long he had taken to get off the mark, Kane said: “Maybe a minute? Eighty seconds? Hey, it’s not too bad!
“It’s the start I dreamed of, it’s a little bit of a blur at the minute. It’s the best moment by far, to represent your country at senior level is the top. Hopefully I can keep doing it and it’s the first of many.”
It was a dream start which impressed then England captain Rooney – a man who knew a thing about coping with pressure and scoring goals and whose national-record of 53 goals Kane surpassed in March 2023.
“It’s fantastic, international football’s different and to score after 80 seconds is incredible for Harry,” he told ITV. “We’re all delighted and hopefully it’s the first of many.”
All those involved were quick to try and keep a lid on expectations, but given Kane now stands alone at the top of England’s goalscoring charts, they clearly knew what they were seeing.
“It is fantastic for Harry,” manager Roy Hodgson said. “We’re so delighted for him. It is a bit of a fairytale, but it’s nice when fairytales come true and it’s come true for Harry.”
“He’s crowned his England debut with a well-taken goal. Couldn’t be better really. It’s a very satisfying evening for us. I think it’s too early to put this pressure on Harry Kane. We should just be happy that he has done so well for Tottenham and made a name for himself to get into the England set-up.
“That’s not easy to do as we have a number of good forwards but let’s be happy with that and leave the future predictions to the future.”
