The Euro 2016 semi-finalists initially faced spirited Moldovan resistance but led 2-0 at half-time thanks to goals from Sam Vokes and Joe Allen.
Gareth Bale seized on a woeful pass for the third, then netted a last-minute penalty for his second of the night.
Wales' win puts them top of Group D on goal difference ahead of Austria.
Chris Coleman's men travel to Vienna for their next World Cup qualifier on Thursday, 6 October.
As the group's top seeds, Coleman's side had been expected to make light work of Moldova, who are ranked 154 places below them in the world rankings.
After a cagey first half hour they eventually did so with a flourish, becoming the first team to score three or more goals against the eastern European minnows since England's 4-0 victory in 2013.
Having led Wales to a first major tournament semi-final at Euro 2016, Coleman said he was "desperate" to follow that achievement by qualifying for the 2018 World Cup in Russia.
The former Fulham manager and his players want to ensure their summer exploits in France were not a one-off but a springboard to sustained success.
They were backed by a typically vociferous Cardiff City Stadium crowd of 31,731, close to capacity once again as a nation basks in its greatest footballing era.
And although it came against limited opposition, this opening victory was an encouraging start as Wales aim to end an absence from World Cups that stretches back to 1958.
"That was the perfect start," former Wales international John Hartson said on Radio 5 live. "Moldova were awful, it was a comfortable win as you will see and great start to the qualifying campaign."
There was a familiarity to Wales' initial inability to break Moldova down; struggling to unlock a deep and tenacious defence as they had done against Andorra and Israel during their Euro 2016 qualifying campaign.
Moldova had lost 14 of their past 20 games but they are seldom pushovers and have conceded only 26 goals in the process.
However, Wales' domination of possession and territory eventually paid dividends after 38 minutes when Bale's arcing cross was headed in by Vokes.
Five minutes later, a weak attempted clearance from Moldova goalkeeper Ilie Cebanu found its way to Allen, who scored his first goal for Wales with a drilled half-volley from the edge of the penalty area.
Bale claimed Wales' third goal in comical circumstances, as he latched on to a terrible backpass from Moldova's Ion Jardan before clipping the ball neatly beyond Cebanu.
The Real Madrid forward scored his second in added time, converting a penalty after he had been brought down to move within four goals of Ian Rush's Welsh record of 28.
Wales' next fixture could be the toughest of their qualifying campaign, away against Group D second seeds Austria on 6 October.
Austria won 2-1 in Georgia on Monday and, with Serbia and the Republic of Ireland drawing 2-2 in Belgrade, this group is expected to be wide open.
Sterner challenges await Coleman's side but this victory - their biggest winning margin in a competitive game since 2003 - will lift hopes of qualifying for a first World Cup in 60 years.
Match ends, Wales 4, Moldova 0.
Second Half ends, Wales 4, Moldova 0.
Goal!  Wales 4, Moldova 0. Gareth Bale (Wales) converts the penalty with a left footed shot to the bottom left corner.
Penalty Wales. Gareth Bale draws a foul in the penalty area.
Penalty conceded by Andrian Cascaval (Moldova) after a foul in the penalty area.
Offside, Wales. Gareth Bale tries a through ball, but Andy King is caught offside.
Attempt saved. Hal Robson-Kanu (Wales) left footed shot from the left side of the box is saved in the centre of the goal.
Gareth Bale (Wales) wins a free kick in the defensive half.
Foul by Andrei Cojocari (Moldova).
Joe Allen (Wales) wins a free kick in the defensive half.
Foul by Aleksandru Gatcan (Moldova).
Hal Robson-Kanu (Wales) wins a free kick on the left wing.
Foul by Andrian Cascaval (Moldova).
Foul by James Chester (Wales).
Igor Bugaev (Moldova) wins a free kick in the defensive half.
Offside, Moldova. Maxim Mihaliov tries a through ball, but Eugeniu Sidorenco is caught offside.
Substitution, Moldova. Maxim Mihaliov replaces Alexandru Dedov.
Emyr Huws (Wales) wins a free kick on the right wing.
Foul by Igor Armas (Moldova).
Substitution, Wales. James Collins replaces Ashley Williams.
Attempt missed. Andy King (Wales) right footed shot from outside the box is close, but misses to the right. Assisted by Emyr Huws.
Attempt missed. Igor Armas (Moldova) left footed shot from outside the box is too high. Assisted by Ion Jardan.
Substitution, Moldova. Igor Bugaev replaces Radu Ginsari.
Substitution, Moldova. Eugeniu Sidorenco replaces Eugeniu Cebotaru.
Substitution, Wales. Hal Robson-Kanu replaces Sam Vokes.
Attempt missed. Gareth Bale (Wales) left footed shot from outside the box misses to the left. Assisted by Emyr Huws.
Corner,  Wales. Conceded by Alexandru Epureanu.
Corner,  Wales. Conceded by Alexandru Dedov.
Corner,  Wales. Conceded by Alexandru Epureanu.
Attempt blocked. Andy King (Wales) right footed shot from outside the box is blocked. Assisted by Joe Allen with a headed pass.
Substitution, Wales. Emyr Huws replaces Joe Ledley.
Foul by Joe Ledley (Wales).
Radu Ginsari (Moldova) wins a free kick in the attacking half.
Offside, Moldova. Ion Jardan tries a through ball, but Radu Ginsari is caught offside.
Joe Ledley (Wales) wins a free kick in the attacking half.
Foul by Andrei Cojocari (Moldova).
Joe Ledley (Wales) wins a free kick in the attacking half.
Foul by Andrei Cojocari (Moldova).
Delay over. They are ready to continue.
Delay in match Sam Vokes (Wales) because of an injury.
Wales started their 2018 World Cup qualifying campaign in confident fashion as they convincingly beat Moldova.