Such was the injury toll, Miah Nikora had to step in at scrum half as the province knuckled down to see out a gritty win that was capped off by a late breakaway try from Mike McCarthy.
Nikora was hugely influential, landing all six of his place-kicks for a 15-point return, and there were noteworthy performances from try scorers Tiernan O'Halloran and George Naoupu along with Denis Buckley, who had another solid shift in the scrum, and Eoin Griffin.
Gavin Duffy took the man-of-the-match honours for a strong showing, particularly in defence where his positioning was key in foiling a number of Zebre attacks.
Elwood used all 23 players in his matchday squad and speaking afterwards, Connacht captain Duffy acknowledged the hard work of his team-mates in securing an important result for the westerners.
"I think it was a good display in the first half and although we suffered from injury in the second half, we battled well throughout the game," he said.
"It was a combined effort from the entire squad. At times, it wasn't pretty but we got the win and the four points and that's the important thing."
The pressure was on Connacht to open their win account after failing to do so at home to the Cardiff Blues last week. With current table toppers, the Scarlets, visiting them in round 3, they will need to make another step up.
Reflecting on the performance in Parma, the province's backs coach Billy Millard explained: "We controlled things well in the opening half and corrected a lot of the mistakes from last week.
"The second half was a bit scrappy with a lot of reshuffling of players due to injury and Miah having to step in at number 9. But the guys did really well to hang in there for the win and we're all very happy (with the result)."