John Muldoon came off the bench and skippered Connacht to a bonus point win in awful conditions at the Sportsground.
The champions were leading 12-3 but were struggling to put the basement side away against the wind and rain.
But Muldoon steadied the ship and guided them home, tapping a penalty and driving over for Connacht's third try before another surge four minutes later wrapped up the bonus point after 66 minutes through a penalty try.
Both teams struggled in the difficult conditions and Connacht had a bit of work to do when they only led 12-0 at the break, having played with the elements.
The champions got an early boost when Niyo Adeolokun struck for the opening try after seven minutes.
It came from a five-metre penalty in front of the posts which was worked wide through half-backs John Cooney and debutant Steve Crosbie for Adeolokun to score his fifth try of the campaign in the right corner.
Cooney added the difficult conversion from the right but it took Connacht some time to build on their lead.
Flanker Eoin McKeon had a try disallowed for an infringement before another back-row Naulia Dawai crossed after 26 minutes.
Zebre got on top after the restart but while Guglielmo Palazzani pulled back a penalty, he was off target from in front of the posts.
Then the visitors' replacement tighthead Bart Le Roux knocked on as he tried to score but once Muldoon entered the fray, Connacht took charge.
Kieran Marmion, just back from a HIA, created the opening with a superb break from deep and when Zebre offended in front of their posts, Muldoon did the rest.
And after getting the bonus point, they completed the rout when Lewis Stevenson got their fifth try.
Connacht - T O'Halloran (C Ronaldson 71); N Adeolokun, T Farrell, B Aki, S Ili; S Crosbie (J Carty 63), J Cooney (K Marmion 40-54, 59); R Loughney (D Buckley 54), T McCartney (D Heffernan 71), D Robertson-McCoy (F Bealham 54); L Stevenson, A Browne (Q Roux 68); E McKeon, N Dawai, E Masterson (J Muldoon 57).
Zebre - D Berryman (C Engelbrecht 71); M Bellini, T Boni, T Castello, L Greeff; S Bordoli, G Palazzani; B Postiglioni (A de Marchi 57), O Fabiani (T d'Apice 59), D Chistolini (B le Roux 49); Q Geldenhuys (M Archetti 67), V Bernabo (J Furno 49); M Cornelli, G Koegelenberg, F Ruzza.
Ref - M Mitrea (Italy).