Eric Elwood's men led 12-6 at half-time, with Daniel Halangahu landing a penalty double for Zebre.

A penalty try should have inspired further tries from the home side, but Halangahu's boot closed the gap for the Italians and winger Ruggero Trevisan's well-executed try set up a tense conclusion at 19-17.

Halangahu's fifth penalty goal had Zebre 11 minutes away from a famous first win, however Parks split the posts on two more occasions for a handsome 20-point haul.

The rain abated before kick-off and the first sign of a Connacht threat came with a 40-metre burst from Robbie Henshaw, who has been called up to the extended Ireland squad.

The teenager full-back's raid forward was a rare moment of excitement in a slow first quarter that lacked any real spark and tempo.

A firm long range penalty strike from Parks edged the hosts ahead, but they were pinged for not rolling away from the restart, allowing Halangahu to bring the Italians level.

Parks answered back with a neatly slotted kick from inside the 22 as Connacht improved their accuracy, using their strong set piece game to dictate proceedings.

Although captain Nathan White was part of a commanding front row, the hosts were unable to hammer home that advantage and relied again on the boot of the fit-again Parks.

The former Scotland international drilled over a drop goal while he had a penalty advantage to move the westerners 9-3 clear.

But Connacht's own errors gave the Italians the opportunity hit back swiftly, and Australian Halangahu stepped up to split the posts from distance.

Giovanbattista Venditti, who was tidy in his clearing and covering, and Mauro Bergamasco, the heartbeat of the visitors' pack, led the pool's bottom-placed team in terms of work-rate.

With the try-lines remaining unthreatened at both ends, a third successful penalty from Parks put six points between the sides at the break.

Parks kicked Connacht to within five metres of the whitewash early in the second period, and the pressure took it toll.

Zebre leaked a penalty from the ensuing lineout maul and then two scrum infringements, with White, Jason Harris-Wright and Brett Wilkinson dominating their front row opponents, led to a penalty try.

Parks converted but there was no sign of Zebre wilting as Bergamasco willed his team-mates forward and Connacht indiscipline gave them further scoring chances.

Halangahu continued his strong showing with the boot, firing over a quick-fire penalty brace after 49 and 51 minutes.

The Italian outfit pressed for a try shortly afterwards, going close through their forwards with replacements David Ryan and Matias Aguero solidifying their scrum initially.

Zebre's sudden resurgence almost erased Connacht's lead as they broke from a scrum on the 10-metre line, centres Roberto Quartaroli and Matteo Pratichetti punching the hole which led to Trevisan scoring out wide.

The difficult conversion was missed by Halangahu, leaving Connacht just two points ahead with Parks suffering his first miss entering the final quarter.

Halangahu's lead score in the 69th minute set up a nervy finish, but a ruck offence ensured that Parks restored Connacht's advantage just two minutes later.

Then a strong run from man-of-the-match Henshaw helped set up the insurance score - a second drop goal from Parks - as Connacht triumphed in Elwood's last European match in charge of the province.