Matt Healy and Robbie Henshaw both bagged tries as Connacht easily saw off Italian visitors Zebre 20-3 at The Sportsground.
Healy's touchdown and the accurate boot of Jack Carty gave the Irish province a 13-3 advantage at half-time.
Luciano Orquera's penalty was the Italian side's response before the interval, but they couldn't build on it after the break as Henshaw went over for the Galway-based outfit to seal the win.
Despite having two top European sides in their pool in Toulouse and Saracens, Connacht's shock victory over the French giants in round three kept their faint hopes of qualifying alive.
However, they made a slow start to this encounter against the Italian minnows. Although Carty missed an opportunity to put the hosts in front, it was the visitors that did most of the early running.
On ten minutes, Orquera deservedly gave them the advantage via a penalty before the home side's stand-off levelled matters with one of his own.
Filippo Ferrarini was then sin-binned for Zebre as Pat Lam's men increased the pressure and Carty took them into a 6-3 lead.
That extra man was to prove decisive when Healy superbly finished off a move to take Connacht into the break 13-3 ahead.
The Irish team continued to dominate in the second period and just three minutes into the half, Henshaw crossed the whitewash.
Healy nearly touched down for their third try but lost the ball forward in the process of scoring, and then intercepted a stray pass late on only to be held up.
That was Connacht's final opportunity as they missed the chance to take the try bonus-point they desired.
Tries: Healy, Henshaw
Cons: Carty 2
Pens: Carty 2
Yellow Card: Ferrarini
Connacht: 15 Darragh Leader, 14 Fionn Carr, 13 Robbie Henshaw, 12 Eoin Griffin, 11 Matt Healy, 10 Jack Carty, 9 Kieran Marmion, 8 Eoin McKeon, 7 Jake Heenan, 6 John Muldoon (capt), 5 Andrew Browne, 4 Mick Kearney, 3 Nathan White, 2 Sean Henry, 1 Brett Wilkinson
Replacements: 16 Jason Harris Wright, 17 Denis Buckley, 18 Rodney Ah You, 19 Michael Swift, 20 George Naoupu, 21 Paul O'Donohoe, 22 Dan Parks, 23 Gavin Duffy,
Zebre: 15 Gullo Palazzani, 14 Giiulio Toniolatti, 13 Kameli Ratuvou, 12 Gonzalo Garcia, 11 Dion Berryman, 10 Luciano Orquera, 9 Alberto Chillon, 8 Samu Vunisa, 7 Dries van Schalkwyk, 6 Filippo Ferrarini, 5 George Biagi, 4 Quintin Geldenhuys (capt), 3 Dario Chistolini, 2 Davide Giazzon, 1 Matias Aguero.
Replacements: 16 Tommaso D'Apice , 17 Andrea de Marchi, 18 David Ryan, 19 Marco Bortolami, 20 Nicola Cattina, 21 Roberto Quartaroli, 22 Ruggero Trevisan, 23 David Odiete,
Referee: Neil Paterson (Sco)