Ollie Thorley scored four first-half tries before Gloucester held off a second-half Leicester fightback to win.
Tries from Joe Simpson and Thorley set the tone as Gloucester's backs played some excellent running rugby.
Thorley scored three more and Chris Harris dotted down before Harry Potter pulled a try back before the break.
Tigers' Jordan Taufua and Cameron Henderson both crossed and George Ford's penalty got them close before Lloyd Evans sealed Gloucester's win.
Gloucester stay eighth, one point behind Harlequins and eight off the top four, while Leicester remain 11th, three points behind 10th-placed Worcester with Saracens already relegated.
Gloucester's 36-point first-half haul was the biggest in the club's history - beating the 35 points they put on Bath at Kingsholm in their biggest-ever Premiership win in May 2002.
Thorley was at the heart of it with the quickest-ever quartet of Premiership tries adding more fuel to those calling for the 23-year-old to win a first England cap.
Leicester struggled to cope with the quick passing of Gloucester's backs as first Simpson went over and then Thorley put Leicester to the sword - the speedy winger completed his hat-trick in a 15-minute spell of almost faultless passing play as veterans Danny Cipriani and Billy Twelvetrees pulled the strings.
Thorley's fourth saw him pick up the ball 10 metres inside his own half and fly past Leicester's defence on 29 minutes to score in the right corner, and with it become just the third player to score four tries in the first half in a Premiership match after Wasps' Christian Wade and Bath's Tom Voyce.
Harris ran half the length of the field after good work by Jake Polledri for Gloucester's sixth try, but the tables turned when Tigers brought on England centre George Ford for 21-year-old Tom Hardwick five minutes before half-time.
Just a minute later the visitors scored their first try as the impressive Zach Henry broke through the Gloucester line and fed Potter to go over unchallenged.
Leicester were a much better side after the restart as Ford's experience and that of England scrum-half Ben Youngs and forward Taufua - who were both half-time replacements - gave confidence to a young starting side.
They were rewarded when Taufua went over from close range on 54 minutes before Cameron Henderson scored a similar try five minutes later.
Ford added a penalty soon after to close the gap to a converted try following 24 unanswered Leicester points, but Billy Twelvetrees' penalty with 10 minutes to go increased the gap to nine points.
Gloucester made sure there were to be no further alarms as Evans broke through from 25 metres for his side's seventh try as the Cherry and Whites finished with their highest-ever score against Leicester.
Gloucester attack coach Alex King on uncapped wing Thorley: "His work with Jonny May and the other wingers at the club is crucial to how we want to play.
"Ollie scored four today, but the work of Jonny and (full-back) Jason Woodward was outstanding as well. It is a collective effort.
"We lost a little bit of control in the second half, but I am really proud of the boys that they found a way to win.
"Sometimes it is hard to get momentum back when you have lost it, and we need to look at why that happened. Rugby can be like that sometimes. We have all watched games and been in games when teams come back into it."
Leicester director of rugby Geordan Murphy told BBC Radio Leicester: "We didn't put ourselves in a position to win without a lot of hard work, so I think there are some really pleasing things.
"We were very disappointed with the first half. We've picked a very young, inexperienced side and the goal was to compete, to fight and to work very hard for each other and we did that - it was just a shame that we gave Gloucester such a head start.
"They scored some very good tries and their backline hurt us in the first half and second half we made some adjustments and I thought there were some very pleasing performances.
"Ollie Thorley's a world-class finisher and to see him get four was slightly frustrating and I thought the coaching group did a really good job at half adjusting and the second half was a completely different story."
Gloucester: Woodward; Thorley, Harris, Twelvetrees, May; Cipriani, Simpson; Rapava-Ruskin Singleton, Balmain, Slater, Garvey, Ackermann, Ludlow (capt), Polledri
Replacements: Marais, Fourie, Stanley, Reid, Clement, Varney, Seabrook, Evans
Leicester: Worth, Potter, Porter, Hardwick, Olowofela, Henry, Van Poortvliet; Bower, Clare, Heyes, Lavanini, Enever, Chessum, Smith (capt), Coghlan
Replacements: Kerr, Gigena, Leatigaga, Henderson, Taufua, B Youngs, Ford, Kelly.