NewsLoan watch: Koumas and Stephenson on target as five Reds see action
Koumas was on target for Stoke City as they were beaten 2-1 by West Bromwich Albion in the Championship, while Stephenson netted for Dundee United in a 2-0 win over St. Johnstone in the Scottish Premiership.
Koumas – who was deployed centrally – struck a leveller for Stoke with a well-taken low finish from inside the box after Karlan Grant had given the visitors an earlier advantage.
Josh Maja went on to earn the Baggies all three points, while Koumas also struck the woodwork twice for the home side in a close encounter.
"[It was] unbelievable," Koumas reflected post-match. "It was a great feeling scoring my first Championship goal and something that I manifested throughout the week.
"It felt electric and it obviously fills me with confidence to go on and score again."
Stephenson, meanwhile, opened the scoring for Dundee United at Tannadice Park by hitting home a rebound in the area before a Jack Sanders own goal sealed the spoils late on.
"Absolutely brilliant, [I] loved it!" Stephenson said afterwards. "We got off to a bit of a shaky start, but I thought the second half was brilliant. I thought the team were class and what a feeling [to score]!
"A first professional goal in my first league game, [you] can't beat it."
Elsewhere, Luke Chambers completed the full match in Wigan Athletic's 1-0 home victory over Crawley Town in League One, while Rhys Williams and Morecambe were beaten 1-0 by Doncaster Rovers away in League Two.
Fabian Mrozek was in goal for IF Brommapojkarna on Sunday when they suffered a 2-1 defeat away at AIK.
VideoInside Training: Watch head-to-head sprints, competitive rondos and more
NewsMohamed Salah voted Liverpool's Men's Player of the Month
NewsSalah and Van Dijk included... Jamie Carragher picks his all-time Liverpool XI
Gallery54 training photos as Liverpool prepare for Bournemouth clash
News'Just getting better' – Thiago thrilled to see Ryan Gravenberch evolution