Wales left it late to beat lowly Moldova as goals from Hal Robson-Kanu and Aaron Ramsey gave them a second win in four days to keep their hopes of qualifying for the 2018 World Cup alive.
Wales had revived their prospects of qualifying with a dramatic win over Austria in Cardiff three days earlier, as Woodburn came on to score a fabulous long-range goal just four minutes into his international debut.
The Liverpool forward remained on the bench in Chisinau, although manager Chris Coleman signaled his attacking intent by switching from his favoured 5-4-1 formation to a 4-2-3-1 system as he had done at half-time against Austria.
Despite a gulf of 141 places between the two nations in the Fifa world rankings, the game was goalless at half-time thanks to a combination of stubborn Moldovan defending and a dearth of quality in the Welsh attack.
Just as their desperate search for a winning goal seemed destined for crushing disappointment, the visitors were again left to cherish the impact of Ben Woodburn, their match-winner against Austria on Saturday, as the 17-year-old's superb run and cross set up Robson-Kanu's diving header.
Ramsey's deflected strike in injury time sealed victory for Wales, who are now up to second place in Group D but remain four points behind leaders Serbia, who beat the Republic of Ireland in Dublin.
With only two matches left, that means the play-offs look like Wales' likeliest route to next year's tournament in Russia.
The play-off places will be filled by the eight best runners-up in the nine qualifying groups, excluding their results against the bottom side.
As things stand, although Wales' chances of qualifying automatically as group winners are all but over, their victory against Moldova at least means they have stolen a march on the Republic of Ireland in the race for second spot.