The German side's one-goal advantage from a controversial encounter last week was wiped in the opening 10 minutes as Lucas Paqueta found the back of the net.
The Hammers were soon in front following a brilliant effort from England international Jarrod Bowen, with the momentum firmly swinging in the hosts' favour.
David Moyes's men added some sparkle to an exceptional display in East London, with an Aaron Cresswell goal and Mohamed Kudus's brace sealing a five-goal success.
Having won the Europa Conference League last season, West Ham are still on course for back-to-back continental triumphs and will discover their quarter-final opponents on Friday.
After being largely unconvincingly during their 2-2 draw with Premier League strugglers Burnley on Sunday, West Ham made four changes to the side that started against Vincent Kompany's Clarets.
James Ward-Prowse was taken out of the firing line following criticism from sections of the fanbase, whilst Michail Antonio was rafted in to lead the line.
As for the visitors, Freiburg made just the single alteration from the XI which defeated VfL Bochum in the Bundesliga on the weekend, with midfielder Lucas Holer replacing last week's matchwinner Michael Gregoritsch.
West Ham took little time to right the wrongs of the first leg at Europa-Park Stadion and were level in the contest after just eight minutes at the London Stadium, where Brazilian Paqueta was the first name onto the scoresheet.
Towering Czech Tomas Soucek managed to get a glancing touch at the near post from an Cresswell corner-kick delivery, and the ball found its way to the onrushing Paqueta at the back, with the 26-year-old sliding in to bundle his effort past Noah Atubolu in visitors' net.
With the early leveller for the Hammers setting the tone for the contest, it was not long before the Premier League side had taken the lead in the tie overall, with Bowen finding the net in Europa League for the first time this season.
Antonio decision to let the ball run past him allowed Bowen a run at Christian Streich's backline just outside the box, and the 27-year-old bullied Freiburg captain Christian Gunter to the ground before unleashing a low-driven strike into the bottom-right corner, leaving youngster Atubolu helpless in net.
Looking to change their fortunes in the second period, the Germans introduced Austria international Gregoritsch off the bench in place of Vincenzo Grifo, however the presence of an extra striker on the field for Freiburg failed to pay dividends as the Hammers ran away with the contest.
Finding himself in acres of space just outside of the box on the left, West Ham veteran Cresswell had the luxury of taking a preparatory touch before firing his effort into the far corner to make it 3-0 on the night, with the 34-year-old scoring his first-ever European goal.
If the fixture had not already been entertaining enough for the jubilant London Stadium crowd, former Ajax attacker Kudus was the next West Ham player to get in on the goals, with the Ghana international running from inside his own half and eventually slotting the ball past Atubolu.
Kudus completed a marvellous night in the capital for Moyes's side with his second of the match in the final five minutes, sending a driven strike past the attentions of the Freiburg goalkeeper after being set up by Bowen on the edge of the box.
More to follow.