Wales coach Robert Page named Gareth Bale on the left wing as the Real Madrid attacker was one of three Wales survivors in the starting line-up from the 2016 semifinal loss to Portugal.
Switzerland boss Vladimir Petkovic kept Benfica's Haris Seferovic and Borussia Moenchengladbach's Breel Embolo up front despite Mario Gavranovic scoring four times in two pre-tournament friendlies.
With Petkovic naming a narrow back three, Bale and fellow winger Dan James found space out wide early on in front of an estimated 10 000 crowd as local authorities allowed up to 50-percent capacity in the 69 000-seater Olympic Stadium.
After a quarter of an hour played, James broke free down the left before finding 1.95 metre-tall Moore who forced Swiss goalkeeper Yann Sommer to tip the ball over the bar.
From the resulting corner, Moore rose highest again and clashed in the air with Manuel Akanji, which left the Cardiff forward playing the remainder of the game with red tape around his head.
With Moore bandaged, the momentum swung towards Petkovic's side and they dominated the remainder of the half but Seferovic wasted three chances.
Moore returned after the interval despite completing just one of his team's 101 passes in the first half.
Petkovic's Switzerland, who reached the last 16 five years ago, remained in control with captain Granit Xhaka, Liverpool's Xherdan Shaqiri and Atalanta's Remo Freuler dominating midfield.
- Embolo sparks to life -They broke the deadlock four minutes into the second half as Embolo sparked into life after a quiet opening 45 minutes.
He broke down the middle and forced Danny Ward into a save, which gave Shaqiri a corner on the right flank.
He delivered to Embolo who headed home after beating Wales right-back Connor Roberts with ease for just his sixth goal in 44 international appearances.
Shaqiri, who played just 14 Premier League games for Liverpool last season, was substituted on 66 minutes for the more defensive Denis Zakaria.
Despite Petkovic's pragmatic change in personnel, Wales equalised with 16 minutes remaining.
Manchester United's James played a corner short which ended up at Joe Morrell's feet and he crossed into the box.
Moore lost his marker and headed a well-placed effort passed the out-stretched Sommer to send the roughly 300 travelling Wales fans into a frenzy behind the opposite goal.
James was then replaced by David Brooks as both sides searched for a winner.
Seferovic was substituted for 31-year-old Gavranovic on 84 minutes and the Dinamo Zagreb forward thought he had claimed all three points for his side with his first touch.
After edging past the Wales backline he beat Ward but his effort was chalked off for offside by VAR.
Switzerland pressed on in five minutes of injury time and Gavranovic was denied another potential winner, this time Ward saving with his finger tips.
Ramsey left the field for Ethan Ampadu during time added on and Page's men held on for a point.
Wales stay in Baku for their next game when they face Turkey on Wednesday, with Switzerland taking on Italy in Rome later that day. (AFP)

SWAN Honours Ezeonwuka, 40 Years After Building Rojenny, Nigeria’s First Private Stadium
Man City need to 'step up' as striker's goal run ends
'People are afraid' - why 'juggernaut' Arsenal are team to beat
Aspinall requires further tests on eye injury in UK
Real Madrid impress but Vinicius tension grows - Clasico talking points
Rooney says struggling Liverpool lack leadership
NOC To Host FinalIOC Advanced Sport Management Course Module
4 Teams Lock Horns For N10m Tiger 5-Aside Football Battle In Awka
Nezianya, Odikpo, Balepo, Ndukuba, Chukwuleta For SWAN @60 Veterans’ Awards
Anambra FA Crisis: Igbokwe, 61 Years Old Football Administrator Protests Arrest, Detention
Gala European record thrills Osimhen
La Liga: 'I am enjoying football at Barca', Rashford eyes permanent move
Rangers International going, going . . . (63,273 views)
Amaju Pinnick: A cat with nine lives (54,479 views)
Second Term: Amaju Pinnick, Other NFF Heavyweights Home to Roost •How Pinnick Broke the Jinx (52,428 views)
Current issues in Nigerian sports: Matters arising (52,036 views)
Sports Development: Zenith Bank on the zenith (52,015 views)
Missing $150,000 IAAF Grant: Solomon Dalung’s Hide and Seek game (51,988 views)
Gov. Abdullahi Ganduje’s solid footprints, commitment to sports development in Kano State (51,818 views)
NFF Presidency: Pinnick, Maigari, Ogunjobi, Okoye in Battle for Supremacy (51,398 views)
Olopade, BET9A wave of revolution in NNL (50,512 views)
Commonwealth Games 2018: Shame of Muhammadu Buhari, Solomon Dalung (49,052 views)
Ibrahimovic’s Man U exit: Whose decision is it? And in whose interest? (47,491 views)
John Mikel Obi: Segun Odegbami’s Outrageous Call! (46,953 views)