The provincial rivals shared four tries in a energetic first 18 minutes with George Naoupu running in an opportunist effort to get Connacht off the mark before Olding, with his fourth try in six games, and Andrew Trimble replied for the Ulstermen in rapid fashion.
Fetu'u Vainikolo was next over the try-line for Connacht with Dan Parks' conversion bringing the sides level at 12-12.
A penalty apiece from Parks and Ruan Pienaar followed before Rory Best grabbed Ulster's third try to give them a 22-15 interval lead.
The scoring dried up in a hard-fought second period, a Miah Nikora penalty getting Connacht closer, although the league leaders showed their class late on with Tommy Bowe's bonus point try and a fifth from Jared Payne.
Connacht stuck with the team that won in Edinburgh last weekend, although a dislocated thumb sustained in training forced Robbie Henshaw's late withdrawal.
Ulster welcomed back Payne and Ireland internationals Trimble, Paddy Jackson and Chris Henry, but the visitors got off to a rocky start.
Kieran Marmion hounded his opposite number Pienaar into coughing up possession in the Ulster 22, the alert Brian Murphy swept quick ball away to the left and Mike McCarthy passed for number eight Naoupu to go over unopposed.
Parks was unable to slot the left-sided conversion and Pienaar was wide with a penalty chance to reply, although the Ulster backs soon clicked into gear.
Darren Cave was involved twice in the build-up to Olding's ninth-minute try, first firing out a skip pass and then combining with Trimble and Payne to put the Ireland Under-20 international in behind the posts.
Pienaar converted and as Ulster quickly exploited space down the same right flank, it was the South African's deft backhanded pass that sent Trimble breaking away from Marmion to score in the corner.
The try was unconverted and Connacht hit back by the end of the first quarter, the backs threading a series of passes out for Tongan Vainikolo to cut in impressively past Trimble and Payne.
Parks and Pienaar traded penalties before Ulster, with their big forwards getting on top, moved back in front ahead of half-time.
Stand-in captain Best slipped off an advancing lineout maul to crash over for try number three. Pienaar converted but was just short with a late penalty attempt from near halfway.
Cave and Trimble continued to probe in attack in the second half, while some strong running from Eoin Griffin set up a close-in penalty for Nikora.
The New Zealander duly registered the three points, closing the gap to 22-18 and setting up an evenly contested third quarter.
Defences tightened up and scoring opportunities were few and far between, Danie Poolman doing extremely well to hold up Payne over the Connacht line.
Connacht's resilience was further tested by a series of five-metre scrums with John Afoa adding his weight to the Ulster front row.
The hosts held out initially, but their defence was finally unlocked again when replacement Iain Henderson charged past two defenders and popped a one-handed offload away for Bowe to finish off.
Pienaar added the extras and full-back Payne ran in a fine breakaway try six minutes later.
- Sports & Recreation
- Ruan Pienaar
- Andrew Trimble