In the day’s other friendly matches, Aston Villa were held by Nottingham Forest, Leicester fought back to defeat Birmingham while Everton and Newcastle suffered defeats to Leeds and Borussia Monchengladbach respectively.
At the Olympic Stadium in Helsinki, the Reds left it late to break the deadlock in a game of few clear-cut chances, substitute Origi turning well in the area after a nice flick from James Milner with 15 minutes remaining.
Coutinho made it two five minutes later, collecting a one-two with Milner before his deflected effort nestled in the far corner from 20 yards.
Liverpool remain unbeaten in pre-season, and face Swindon on Sunday in their final friendly before travelling to the Britannia Stadium to face Stoke in the Premier League next weekend.
At the City Ground, Nottingham Forest made a blistering start and broke the deadlock inside 30 second when Dexter Blackstock scored for the hosts, but Aston Villa levelled when Scott Sinclair converted Jordan Amavi’s left-wing cross.
After the break, Sinclair took advantage of a defensive lapse to put the visitors head before thumping in a delicious 25-yard curler.
But the Championship side hit back with two goals inside the final 10 minutes from Henri Lansbury and Kelvin Wilson for a share of the spoils.
At St Andrew’s, Leicester City hit back from two goals down to secure a 3-2 win against Birmingham in another Midlands derby.
David Cotterill and Demarai Gray handed the Blues a perfect start before Foxes boss Claudio Ranieri made three changes at the break which helped turn the tide.
Robert Huth converted Marc Albrighton’s corner kick, before Danny Drinkwater levelled after Riyad Mahrez’s superb free-kick struck the post.
Shinji Okazaki won the game with seven minutes remaining thanks to a flying near-post header from Mahrez’s delivery.
At Elland Road, Leeds United proved too strong for a weakened Everton side, running out 2-0 winners thanks to goals from Alex Mowatt and New Zealand international striker Chris Wood.
The Toffees play Villarreal on Sunday before opening their Premier League campaign at home to Watford next Saturday.
New Sunderland signing Jeremain Lens hit the winner as Dick Advocaat’s side beat Hannover 1-0 in Germany, while Swansea drew 0-0 with Deportivo La Coruna at the Liberty Stadium.
Newcastle suffered a 1-0 defeat to Bundesliga outfit Borussia Monchengladbach at St James’ Park, with Eden Hazard’s brother Thorgan coming off the bench to bag the winner just after the hour mark.
Fulham were held to a 1-1 draw by Crystal Palace in a London derby as Senegal international Pape Souare cancelled out Ben Pringle’s strike.
There was worrying news for Eagles boss Alan Pardew as centre-back Damien Delaney was stretchered off midway through the second half.
Norwich beat Brentford 2-1 at Carrow Road, with Wes Hoolahan and Cameron Jerome scoring for the Premier League side.
Top-flight newcomers Bournemouth were held to a goalless draw against Hoffenheim at the Rhein-Neckar Arena.