But after the break Tommy Bowe and Jared Payne added to earlier tries courtesy of Olding, Andrew Trimble and Rory Best to claim a 34-18 bonus-point victory.
Ulster have just one game remaining and sit atop the table, four points ahead of second-place Glasgow Warriors and eight ahead of Leinster - their Irish rivals having one extra game to play.
This means the Ulstermen look odds on to secure an all-important home semi-final, something 20-year-old Olding believes could prove crucial in the fight for the title.
"Credit to Connacht, they scored a few tries and gave us a scare after 20 minutes or so," said Olding, who made it four tries in six RaboDirect PRO12 games.
"But fair play to our guys as well, they fought back and in the end it was a good performance and good to get the five points.
"It was a hugely physical game. All credit to Connacht, they put in a good performance.
"To back up on our five points last week and then to pick up another five points this week was exactly what we wanted and we have done that and it means we have it in our own hands for the final game."
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