Swansea winger James, making his first competitive start for Wales, struck in just the fifth minute with a goal that ultimately saw the hosts to victory.
"It was a good start after we got that early goal," James told Sky Sports.
"From then on, we had to dig in. The only thing I had in my head was to shoot and luckily it went in."
Wales star Gareth Bale, captaining the side in place of benched regular skipper Ashley Williams, added: "Everyone put in a shift today.
"We built our success off a good solid defence. We work hard in units. We always knew we could nick a goal.
"In the second half we came under a lot of pressure but we started the game well, got the early goal then shut up shop and we know how to do that," the Real Madrid forward insisted.
Giggs rings the changes
Wales manager Ryan Giggs made 11 changes from Wednesday's 1-0 friendly victory over Trinidad and Tobago.
Slovakia, by contrast, were unchanged after beating Hungary 2-0 in their opening qualifier on Thursday.
The Cardiff City Stadium was bathed in sunshine and Wales made an equally bright start.
Harry Wilson and David Brooks combined well down the right but any threat seemed to end when Brooks' pass went straight to Slovakia defender Peter Pekarik.
But Pekarik was then dispossessed on the edge of the box by the 21-year-old James, who then shot powerfully past Newcastle goalkeeper Martin Dubravka to fire Wales in front.
Shortly before half-time Brooks came close to making it 2-0 with a superb solo effort that saw him beat two defenders.
His swerving shot evaded Dubravka only to curl just past the far post.
The only concern for Manchester United great Giggs at half-time would have been that Wales were just 1-0 ahead, with plenty of time left for Slovakia to get back into the game.
Slovakia then created their best chance of the match thus far early in the second half when Albert Rusnak was one-on-one with Wayne Hennessey only for the Wales goalkeeper to block his shot, with the ball rebounding off the Slovakian before it went wide.
Hennessey had to be alert to deny Rusnak a second time before Wales hit back, with Wilson shooting narrowly wide past a beaten Dubravka from James' cross.
Wales found themselves pinned in their own half late on and Slovakia should have equalised with seven minutes left.
Rusnak's cross found Michal Duris, but the substitute's header was tipped away by Wayne Hennessey into the six-yard box rather than clear of danger.
David Hancko, following up, had a superb chance to level from close range but instead miscued his shot completely and that allowed Wales to clear the ball.
The fifth and final minute of stoppage time saw Slovakia awarded a corner following Miroslav Stoch's deflected effort.
But the referee then blew for the end of the match, a decision that saw him surrounded by angry Slovakia players, with Juraj Kucka then booked -- one of seven yellow cards collected by the visitors -- for dissent.
Wales' next two qualifiers are away fixtures against Croatia and Hungary on June 8 and 11 respectively.