Resuming on 336-6, Reece and Thomson extended their eighth-wicket stand to 105 with relatively few alarms and got to within 15 of saving the follow-on.
The new ball saw Timm van der Gugten account for Thomson, but Zak Chappell helped Reece past the target of 282 before Gorvin bowled him to claim his fifth wicket.
Reece passed 5,000 first-class runs for the visitors with a pulled six, before last man Blair Tickner swung wildly to frustrate the struggling Glamorgan attack in a first session extended by 40 minutes.
Resilient Derbyshire even managed a third batting point as the last-wicket stand reached 62 before Tickner (28) was bowled by Asitha Fernando.
On Star Wars Day, the force was with Derbyshire as they claimed three early wickets, having seen their own last three bat for a further three hours on the third day.
The high-stepping paceman Tickner and Anuj Dal swapped ends almost immediately to devastating effect with Asa Tribe, Sam Northeast and Kiran Carlson dismissed in successive overs.
But Ingram’s calmness and the nuggety approach of Ul Hassan saw them put together a patient partnership of 109.
Ingram struck seven fours and lofted Thomson for six but was bowled sweeping at the next ball as the tall off-spinner started to extract turn.
Eight runs later, Chappell got one to lift on Ul Hassan to have him caught behind, and Derbyshire were back in the hunt as they delivered six maidens in a row to end the day.
Glamorgan are currently getting coaching assistance from Ian Harvey, the former Australia all-rounder who was Gloucestershire assistant coach under current Glamorgan boss Richard Dawson.
Meanwhile Jonathan Trott, the former England batter and current Afghanistan coach, is carrying out occasional work as a consultant coach when his international duties permit.
Glamorgan’s Colin Ingram told BBC Sport Wales:
“It’s always nice to spend time in the middle, I came in at a tough period losing early wickets so I enjoyed the challenge, taking a few on the gloves, and had a nice partnership with Zain.
“There’s enough in the wickets for bowlers of both teams but if you do get in there are runs to be had, and they certainly frustrated us this morning because we were hoping for more of a lead.
“They bowled really feistily, the new ball moved around a bit and Blair Tickner bowled really well so the game’s all square which is exciting.
“Hopefully we can put a few more runs together and have a good crack at them in the afternoon.”
Derbyshire’s Alex Thomson told BBC Radio Derby:
“A solid day, starting at 215-7, you would have taken getting 350 with the bat and having them five down at the end.
“It was nice to get stuck in and having the level head of Reesey at the other end helps, it’s put us in a decent position to press on, take some early wickets and see what happens with the chase.
“It’s an interesting final day, we’ve got to come back and try to blast them away or slow them down, and see what we get as a chase.”
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