The Magpies dominated against promoted Nottingham Forest from start to finish at St James' Park on Saturday but were repeatedly frustrated until the Switzerland international finally beat debutant keeper Dean Henderson with a 22-yard rocket 13 minutes into the second half.
Schar's timely intervention provided the foundation for a 2-0 win which might have been significantly more handsome, boosting already-high levels of optimism on Tyneside following a near £150million-and-counting spending spree since Amanda Staveley's Saudi-backed consortium brought an end to more than 14 years of under-achievement under previous owner Mike Ashley.
The defender said: "The fans expect a lot from us this season. It's electric when you are here and you just want to give them something to cheer.
"We have a strong team, a lot of quality, but we know how difficult the Premier League is as well.
"We wanted to start the season well, but we have to focus on the next game and see what happens."
That next game will come at Brighton on Saturday, and Eddie Howe and his players will head south buoyed by a league win at the first time of asking - it took them 15 attempts last season - which was just reward for an enterprising display.
Conducted from central midfield by the imperious Bruno Guimaraes, the Magpies simply had too much for Forest as Allan Saint-Maximin, Miguel Almiron, Joelinton and Joe Willock buzzed around behind striker Callum Wilson, and it seemed only a matter of time before they got their noses in front.
In the event, it took them 58 minutes to find a way past Henderson when Schar took matters into his own hands, and a second from Wilson courtesy of a deft 78th-minute flick cemented the points.
Schar said: "We had a lot of chances and didn't score, so it was an important goal, and it is always great to score in front of the home fans.
"Over the 90 minutes, we played some great football - the goals didn't come in the first half, but we dominated possession and had a lot of chances."
It proved a sobering afternoon for Forest, who did not force new Newcastle keeper Nick Pope into a single meaningful save, but head coach Steve Cooper, who masterminded their return to the top flight after an absence of 23 years, was philosophical in defeat.
Cooper, who started six of his summer signings and introduced two more from the bench, said: "Where we weren't right was our in-possession game. We turned the ball over too much and we didn't make enough passes when we could and, in the end, that's cost us even with the two goals.
"That's the bit where I'm thinking about we fell short in our performance and we have to live and learn from that."