Wasps ran seven tries past Newcastle to win 44-38 and secure seventh spot in the final Premiership standings and thus a shot at a place in Europe.
Wasps will now face Stade Franšais in a two-leg play-off for the final berth in the European Cup next season.
Four tries in 20 minutes before half-time turned this contest on its head as Wasps emerged narrow victors.
Wasps were looking to bounce back from defeat to Bath and an inconsistent run of form, while the Falcons were seeking to address a torrid run of defeats.
But it was the visitors who made a lightning start to the contest, scoring 17 points in the first 15 minutes to establish a healthy advantage.
Sinoti Sinoti laid the platform for Mike Blair to cross in the first minute. Joel Hodgson converted the try and added a penalty before Alex Tait made a spectacular break and found Hodgson who crashed over.
Hodgson converted his own try but Wasps roared back into the contest before half-time.
Nathan Hughes crossed in the corner for the hosts after the pack had laid the platform, and though the conversion was missed Wasps were in again shortly after Ashley Johnson grounded the ball beneath the rolling maul, and this time Andy Goode added the extras.
The home onslaught then continued through Goode's penalty, which narrowed Newcastle's advantage to just two points, before Hughes added his second five points before half-time and then Joe Simpson went over following a neat chip and chase by Elliot Daly.
Two tries in the period after half-time kept the Falcons in the contest, however, with a converted double from Noah Cato making it 29-31 and sealing a bonus point.
But again Wasps found a way back in, and they retook the lead through Will Helu, who claimed Goode's cross-field kick to score.
Goode then booted the hosts further in front with a penalty and they had a cushion when Charles Hayter converted his own score ten minutes by the end, making it 44-31 with time ticking away.
Newcastle had the final say through George McGuigan's converted try, but it counted for little at the end of an entertaining contest.
Tries: Hughes 2, Johnson, Simpson, Helu, Hayter
Cons: Goode 3, Hayter
Pens: Goode 2
Yellow cards: Hayter, Haskell
Tries: Blair, Hodgson, Cato 2 , McGuigan
Cons: Hodgson 5
Yellow card: Fitzpatrick
Wasps: 15 Andrea Masi, 14 Will Helu, 13 Elliot Daly, 12 Charlie Hayter, 11 Tom Varndell, 10 Andy Goode, 9 Joe Simpson, 8 Nathan Hughes, 7 James Haskell, 6 Ashley Johnson, 5 Tom Palmer, 4 Joe Launchbury, 3 Phil Swainston, 2 Carlo Festuccia, 1 Matt Mullan.
Replacements: 16 Tom Lindsay, 17 Simon McIntyre, 18 Taione Vea, 19 James Cannon, 20 Sam Jones, 21 Charlie Davies, 22 Joe Carlisle, 23 Tommy Bell.
Newcastle: 15 Alex Tait, 14 Noah Cato, 13 Gonzalo Tiesi, 12 James Fitzpatrick, 11 Sinoti Sinoti, 10 Joel Hodgson, 9 Mike Blair, 8 Mark Wilson, 7 Will Welch (c), 6 Richard Mayhew, 5 Dom Barrow, 4 Scott MacLeod, 3 Kieran Brookes, 2 Scott Lawson, 1 Rob Vickers.
Replacements: 16 George McGuigan, 17 Scott Wilson, 18 Oliver Tomaszczyk, 19 Harry Spencer, 20 Andy Saull, 21 Warren Fury, 22 Rory Clegg, 23 Lee Smith.
Venue: Adams Park
Referee: Dean Richards
Assistant referees: Nigel Carrick, Andrew Pearce
Television match official: Sean Davey