Aspinall, in just his 14th professional contest, took the fight to Volkov, who was seeking his 35th UFC victory, and cut the Russian early on.
The 28-year-old from Salford, England, continued his strong groundwork to manoeuvre Volkov into an armlock and secured a swift submission.
"I have been telling everyone I am born for this," Aspinall said in his post-fight interview.
"My secret is self-belief. I believe in myself, my dad, my coaches and my team-mates, they have all believed in me, my brother has been helping me every day."
Aspinall will move up the rankings after an impressive win and is already looking ahead to a return to the octagon.
He said: "We drink beer in the UK, not just Australia - so Mr Tai Tuivasa, next time you come to the UK, let's do it bro."
The UFC returned to London for the first time since 2019 and earlier Liverpool lightweight Paddy Pimblett had got the 20,000-strong crowd off their seats as he defeated Mexican Kazula Vargas with a rear-naked choke in the first round.
The mixed martial arts fighter from Huyton recovered from an early setback to finish the contest after going to ground.
Pimblett used his post-fight interview to respond to the earlier call out from Ilia Topuria, the duo involved in a fracas this week at the hotel where the fighters are staying.
The Liverpudlian, nicknamed 'Paddy the Baddy', also took a swipe at Mark Zuckerberg, having seen his Instagram account closed down several times.
Fellow Merseysider Molly McCann produced a superb spinning back-elbow to knockout Brazilian Luana Carolina in the third round of their flyweight contest to crank up the atmosphere in the arena.
Ipswich featherweight Arnold Allen also made a statement as he took out New Zealander Dan Hooker in an explosive first round after the referee stopped the contest.
Allen extended his UFC win steak to nine fights and now looks set for a showdown with a top-five ranked fighter, calling out American Calvin Kattar.
Icelandic welterweight Gunnar Nelson, who has spent time training in Dublin, scored a unanimous decision win over Japan's Takashi Sato in what was his first appearance in the octagon for more than two years.
Earlier, Topuria had silenced the partisan home crowd with a second-round knockout of Jai Herbert in their lightweight contest.
Following his impressive victory, the German-born Georgian wasted little time to call out Pimblett, the pair's rivalry having spilled over into a war of words on social media following their scuffle.
In Saturday's opening prelim contest, 21-year-old prospect Muhammad Mokaev needed less than a minute to defeat Cody Durden with a choke hold, while Finland's Makwan Amirkhani also produced a first-round submission win over Mike Grundy.
Read more: Six Nations - Final week round-up