Notts slumped to 73-7 before Luke Wood (65 not out) Steven Mullaney (63) shared an eighth-wicket stand of 92.
Onions took 5-56 as the hosts were dismissed for 204 in 54 overs, which meant Yorkshire were crowned county champions for the second year in a row.
Durham closed 30 runs behind on 174-2, with Mark Stoneman making 62 and Scott Borthwick unbeaten on 56
The visitors won the toss and invited Notts to bat on an overcast day and Jake Libby, playing in his first game of the season after recovering from a cruciate ligament injury, fell to Chris Rushworth (2-15) in the first over for a second-ball duck.
Onions got rid of Brendan Taylor and Michael Lumb, both for one, with the hosts slipping to 7-3 in the sixth over and Riki Wessels (13) then became a first wicket for 22-year-old Durham debutant Barry McCarthy (2-51).
McCarthy dropped Mullaney, who was on 41 at the time, in the deep, but later trapped the former Lancashire player leg before.
Wickets continued to fall and it was only the partnership of Mullaney and Wood - who passed fifty for the third time this season - which pushed Notts past 200 and earned a single batting bonus point.
Durham started at pace in their reply with Stoneman and Jack Burnham putting on 78 for the first wicket in 15.5 overs.
Stoneman, who was caught by Mullaney off Jake Ball, and Borthwick, who reached his ninth half-century of the season, then put on a second-wicket partnership of 53 as the hosts reached the close in a strong position.
It meant Notts wicketkeeper Chris Read still requires two dismissals to become the 26th player in history to reach 1,000.

Monday's Dublin meeting is part of an assembly External Affairs Committee inquiry and is on the day the UK begins the process of leaving the EU.
The fear is a "soft" post-Brexit border between Northern Ireland and Ireland could result in more stringent controls at Welsh ports for freight operators.
First Minister Carwyn Jones has warned that could mean job losses.
The Irish Minister for Transport, Tourism and Sport, Patrick O'Donovan, and representatives from the Irish Exporters Association were among those meeting AMs during the Dublin visit.
The UK's formal Brexit negotiations with the European Commission started on Monday in Brussels.
Launching a paper on Brexit and devolution last week, Mr Jones said the question of Ireland was "insoluble" at the moment.
He said Wales had an interest in the border between the north and south of Ireland because of Wales' maritime border with the Republic.
Mr Jones warned a "seamless" border between north and south, twinned with customs checks at Welsh ports, could provide an incentive for trade to avoid Welsh ports.
Freight operators could "go through Cairnryan in Scotland, go through Liverpool and go to Northern Ireland then down rather than mess about in Holyhead, Fishguard and Pembroke", he warned.
"So there are job losses there if we're not careful."
The first minister said the Welsh Government was working with the Irish government on the issue.
Graham Onions claimed a five-wicket haul to help Durham have the better of day one against Nottinghamshire.
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Brexit's impact on Welsh ports is being discussed as assembly members meet Irish politicians and business leaders.