Showing scant regard for their 12-hour flight to Ireland during the week, it was the Bulls who started the brighter as De Klerk dived over in the corner following scrum-half Papier’s burst, with the earlier decision to kick for the corner totally vindicated.
After Johannes Goosen kicked the extras from a tight angle, Connacht struggled to get a foothold into the game and they then found themselves down to 14 men when Jansen was red carded.
The South African side huffed and puffed as the rain poured down in Galway but they had to wait until four minutes before the break before they could make their man advantage pay.
Moodie played a clever chip over the Connacht defence down the right wing, and it was Papier who won the chase to the ball, scooping up and touching down under the posts to allow the simplest of conversions for Goosen.
The second period got off to the worst possible start for the home side when they conceded a sloppy try to Kriel within 90 seconds of the restart.
The big centre charged down the left flank before throwing a dummy pass inside that was bought by home full-back Shane Jennings, allowing the number 13 to race home unopposed from 25 metres, with Goosen again adding the extras from the tee.
South Africa international Moodie capitalised on a poor pass from home number 10 Jack Carty on 55 minutes to race home from all of 60 metres to notch the bonus-point securing touchdown, with the conversion again slotted by the fly-half.
Playing numbers were levelled up on 58 minutes when Bulls number eight Celimpilo saw red for a obvious eye gouge on substitute Hawkshaw.
Hawkshaw popped up with a try of his own four minutes later, when he charged over from close range while home replacement scrum-half Blade also crossed the line five minutes from time as Cathal Forde added his second conversion.
Connacht: Shane Jennings; Shayne Bolton, Piers O’Conor, Cathal Forde, Santiago Cordero; Jack Carty, Ben Murphy; Denis Buckley, Dave Heffernan, Jack Aungier; Joe Joyce (capt), Niall Murray; Josh Murphy, Conor Oliver, Sean Jansen
Replacements: Dylan Tierney-Martin, Jordan Duggan, Sam Illo, Darragh Murray, Paul Boyle, Caolin Blade, David Hawkshaw, Shamus Hurley-Langton.
Bulls: Willie le Roux; Canan Moodie, David Kriel, Harold Vorster, Sebastian De Klerk; Johan Goosen, Embrose Papier; Alulutho Tshakweni, Akker van der Merwe, Francois Klopper; Ruan Vermaak, JF van Heerden; Marcell Coetzee (capt), Cobus Wiese, Mpilo Gumede
Replacements: Johan Grobbelaar, Gerhard Steenekamp, Mornay Smit, Jannes Kirsten, Cameron Hanekom, Keagan Johannes, Aphiwe Dyantyi, Stedman Gans.