Iordache, world all-around silver medallist behind Simone Biles back in 2014, made her return to international competition this week after three years out following an Achilles tendon tear.
After helping Romania to team silver on Saturday, Iordache won three medals in Sunday's apparatus finals - including balance beam and floor gold - to take her tally to 16 at the women's European Championships.
Only Svetlana Khorkina with 20 has won more medals in the competition's history.
Romania has now won 55 gold medals at the event, matching the record tally of the Soviet Union.
For Kovacs, her victories in the vault and uneven bars took Hungary's total to five for the event.
In the vault final, Kovacs won the title after executing a clean double-twisting Yurchenko for a 14.350. She followed that up with a full-twisting Tsukahara to earn a 13.750 and a 14.050 average.
Iordache won the second European vault silver medal of her career, executing the same two vaults as Kovacs and posting a 13.875 average.
Ukraine’s Anastasia Motak was just behind in third with 13.850.
Kovacs continued her winning ways on the uneven bars, posting 13.850 to lead a Hungarian 1-2.
She has now won a medal of every colour at the European Championships after taking all-around silver in 2017 and team bronze Saturday in Mersin.
Team-mate Zoja Szekely was the silver medallist with a 13.550 and Slovakia’s Barbora Mokosova (13.300) taking bronze to win her country’s first ever medal at the women’s European Championships.
Competing last and as the top qualifier from Thursday's competition, Kovacs delivered a competent routine after a slightly hesitation on her opening pirouette. Her performance was highlighted by a stalder piked Tkatchev to Pak salto combination in the middle. She dismounted with a clean double tuck.
Iordache missed out on the podium in fourth, scoring 13.250.
But she rebounded minutes later in the balance beam final, earning a 14.000 for gold. Iordache last won the European beam title in 2013. Her routine Sunday on included a solid back handspring to tucked full twist acro series, a stylish double turn and a triple full dismount.
Team-mate Silviana Sfiringu took silver at 13.800 with Motak third (13.100).
Clearly delighted by her return to the top of the podium, Iordache ran to her coach after the score was posted. The two embraced in a hug, while the coach wiped away tears. The triumph even received praise from legendary Nadia Comaneci who tweeted, "Congrats. Felicitări."
Fittingly, Iordache closed out the competition and claimed her third European title on the floor after scoring a 13.450.
But it was not without drama as Turkey’s Goksu Uctas Sanli, who scored 13.100, thought she had won as Iordache's score came up as 13.050.
Iordache, however, submitted an enquiry as to her difficulty score which the judges raised from 5.2 to 5.6 to give the Romanian the title.
Still, Uctas Sanli's silver is the first medal of any colour for Turkey at the event. Lihie Raz of Israel also achieved a first medal for her country in third, scoring 12.750.
In the junior competition, Romania completed its sweep of the gold medals in Mersin. Ana Barbosu added golds in each of the four apparatus finals to her team and all-around golds from Friday (18 December).