Smith, just a fortnight into his full-time reign as Great Britain coach, will be happier with the result than the scrappy performance at Huddersfield's Galpharm Stadium as Britain go in search of a first Test series win for 14 years.
The Lions struggled to turn their supremacy into points but the negatives were outweighed by the positives, which came largely in the form of new half-back pair Leon Pryce and Rob Burrow and the sparkling efforts of the two new boys.
Burgess, at 18 the youngest Briton to make his debut since Andy Farrell in 1993, looked more like a seasoned international as he continued his meteoric rise to fame.
Super League's young player of the year blotted his copybook by being placed on report for a high tackle which will be scrutinised by the video review panel but it was a minor blemish amid a series of crunching legitimate hits.
Fa'asavalu was a controversial choice for his adopted country but he brought the crowd alive with his trademark blockbusting runs that have made him such a favourite at St Helens.
Pryce and Burrow tormented the Kiwis with their incisive running while Burrow also produced a perfect goalkicking performance after taking on the responsibility from the absent Kevin Sinfield.
With both sides scoring three tries, Britain were indebted to the sure boot of man of the match Burrow, who landed all four attempts in contrast to Lance Hohaia, who managed just one from three.
New Zealand twice held the lead as they atoned for their 58-0 hammering by Australia a fortnight ago, although they clearly missed the creativity of Stacey Jones.
His replacement, Thomas Leuluai, was the Kiwis' best player but it was Britain's all-round game that brought them the deserved spoils.
The Kiwis scored from their first threatening attack with a try that had the Super League hallmark all over it, Bradford centre Shontayne Hape racing on to a grubber kick from Wigan's Leuluai.
Britain enjoyed the lions' share of possession and their new half-backs always looked dangerous but it took the introduction of St Helens impact duo James Roby and Fa'asavalu from the bench to give their attack a cutting edge.
Roby, Super League's man of steel, fumbled the ball over the line after collecting a lucky ricochet before providing the pass from which Fa'asavalu crashed over for his side's first try on 29 minutes.
The Samoan lifted spirits on and off the field with a trademark barnstorming run immediately on his entry midway through the first half and he proved unstoppable from five metres out.
Burrow landed the conversion and increased Britain's lead to 8-4 with a penalty but the Kiwis struck once more seven minutes before the break.
Fa'asavalu blotted his copybook with a handling error and debutant Epalahame Lauaki hacked the ball ahead for Paul Whatuira to touch down despite the valiant efforts of Sean O'Loughlin, a late addition to the starting line-up in place of the ill Sinfield.
Hohaia made up for his earlier miss by adding the conversion to restore the Kiwis' lead by half-time but it was a flattering one.
Pryce's clean break six minutes into the second half ought to have produced its reward but New Zealand captain Roy Asotasi pulled off a last-ditch tackle to deny the supporting Paul Wellens.
Left winger Gareth Raynor was then denied by video referee Ashley Klein for obstructing Leuluai in pursuit of Burrow's kick to the corner but he got the green light shortly afterwards when he got the bounce of the ball.
Debutant full-back Sam Perrett looked to have Burrow's long kick covered but, instead of rolling dead, it took a wicked bounce back into the grateful arms of the onrushing Raynor.
Burgess then made the game safe, taking an inside pass from Pryce who had split the Kiwi defence with another scything run.
Burrow maintained his 100% record by landing his fourth goal and the cushion proved valuable when Hape went over for the Kiwis' third try five minutes from the end.