Yet you could easily understand why he would cherish the memento from a thrilling FA Cup third-round tie so much; the burly striker has had to work hard to get to this point for his new club.
Since making the step up to Championship level in the summer, goals have certainly not been easy to come by for the 27-year-old with just four in 26 appearances before these heroics broke Rotherham United hearts.
However, Eaves’ talent and influence in helping how Hull attack teams has never been under-estimated by head coach Grant McCann and, with some of their other leading lights given a rest on the bench against League One opponents, he was able to play his more natural game in this absorbing Yorkshire derby.
Leading scorer Jarrod Bowen and fellow wideman Kamil Grosicki were left on the bench as McCann made eight changes.
“It’s tough sometimes as, with Jarrod and Kamil in their own right, there is so much quality going forward,” said Eaves, who had a brief spell on loan at Rotherham from Bolton seven years ago.
“I fancy them every time when they go one-versus-one so a lot of the times I’m just anticipating.
“It was a bit of a different dynamic today; a lot of the balls came into the box and that’s my bread and butter really.
“I know if the ball comes in those areas I have the quality to put it in the net.”
That said, it needed the triple introduction of 17-goal Bowen, Poland international Grosicki and Australia midfielder Jackson Irvine in the 61st minute to rescue the Tigers from suffering an FA Cup shock.
At that point, they were losing 2-1 despite Rotherham playing with 10 men since Adam Thompson’s dismissal in the 23rd minute for a horrendous tackle on Keane Lewis-Potter.
The Millers were full of confidence and drive, showing just why they are flying so high in League One, and the numerical disadvantage did not seem to be causing them any discomfort at all.
Before the sending off, Paul Warne’s side had already shown spirit by coming back from Eaves’ 16th-minute opener, a routine finish after Dan Batty had surged into the box and squared for the former Gillingham striker.
They quickly responded with a fine effort from Michael Smith, who turned and rifled in to the top corner from 15 yards out after being given far too much room by the Hull defence.
Furthermore, Rotherham readjusted well following right-back Thompson’s rash challenge and took the lead with a truly stunning goal from Kyle Vassell. On the left corner of the penalty area, the Northern Ireland striker allowed a throw-in to bounce past him before turning to strike a brilliant first-time right-footed shot that left Hull keeper Matt Ingram with no chance.
Like Eaves, Vassell has found goals hard to come by – this was only his third in 40 games for the Millers but, encouragingly, a second in three matches.
The 26-year-old clearly likes the spectacular, too; the other was an acrobatic overhead kick in the 4-0 win over Peterborough last Sunday.
Nevertheless, after Hull huffed and puffed, it was obvious McCann would turn to his bench of considerable strength.
The impact was instant; Bowen found space to deliver a cross for Eaves to nod in his second, although there was long discussions between the officials before it was finally awarded.
Rotherham were incensed, feeling there had been an offside in the build-up. Then came all the expected pressure, wave after wave of attack. Admittedly, the Millers looked like holding on until Reece Burke headed a corner back across goal for Eaves to head in and spark wild celebrations.
He tore his shirt off as he joined the fans in celebration.
Eaves admitted: “That was a moment for me. Unfortunately I couldn’t get my shirt off as quickly as I’d have liked... it went a lot smoother in my head!
“I got it off in the end and it is something I can share with the Hull fans. I’ll cherish it.”
Even then the hosts saw an effort hit a post in the dying moments but there was no salvation.
Herbie Kane, the midfielder who had signed for Hull from Liverpool on a six-month loan on Friday, impressed on debut and Scouser Eaves is certain who he wants in tonight’s draw.
He said: “To play at Anfield with all my family there is the dream. I know Liverpool are in unbelievable form at the minute and club-wise are arguably the best team in the world. But that would be a dream come true so I’ll be watching keenly Monday.”
Rotherham United: Iversen; Thompson, Ihiekwe, Wood, Olosunde; Ogbene (Ladapo 79), Crooks, Barlaser, Wiles; Vassell (Lindsay 72), Smith (Morris 90). Unused substitutes: Price, Clarke, Hastie, Lamy.
Hull City: Ingram; McKenzie, Burke, Tarazolli, Fleming (Bowen 61); Batty (Irvine 61), Da Silva Lopes, Kane; Bowler (Grosicki 61), Eaves, Lewis-Potter. Unused substitutes: Long, Lichaj,McLoughlin, Honeyman.
Referee: Anthony Backhouse (Cumbria).