After a wasteful first half with both teams missing several chances to break the deadlock, Barnes opened the scoring for the hosts in the 63rd minute.
For Newcastle, the deal ends Isak’s three-year spell at St James’ Park, where he has scored 62 goals in 109 appearances for the club.
The 25-year-old will join the Reds in a deal worth an initial £125 million, potentially rising to £130 million with add-ons.
Šeško scored 18 goals in all competitions for RB Leipzig last season.
Liverpool initially approached Newcastle last month regarding the striker and have now followed up with an official bid.
Champions Liverpool face Bournemouth in the season’s opening match as league organisers release the matchday schedules for the upcoming season.
Tottenham went into Thursday’s match with a one-goal advantage after they beat Liverpool in the first-leg tie at the Tottenham Stadium.
Arsenal moved second on the league standings after the Gunners secured a dominant 5-2 away win against West Ham United in their Premier League tie at the London Stadium on Saturday
Building on last weekend’s 3-1 win over Newcastle United, Fulham climbed to sixth in the standings on 11 points after six games.
Despite Villa’s late surge, Newcastle’s defence held firm, securing their first league win since mid-December.
