The £9.5million Nigerian hitman struck for the 14th time this season midway through the second half for the only goal of the game to seal victory in a tie that was as good as ended a week earlier when Newcastle won 3-1 in Ghent.
Under the watchful eye of England manager Steve McClaren, Newcastle were always in control and in the last 16 will now meet AZ Alkmaar who are currently lying third in the Dutch League.
Having drawn 3-3 in Istanbul in their first leg against Fenerbahce, last season's UEFA Cup semi-finalists must have feared the worst when they trailed 2-0 against the Turkish side before clawing it back to 2-2 to go through on the away goals rule.
Those ties will be played on 8 March at St. James' Park with the second leg in Alkmaar six days later.
Nolberto Solano became only the 25th player in the history of Newcastle to make 300 appearances for the club - some 196 games behind record holder Jimmy Lawrence.
And with the little Peruvian only two goals away from the 50 mark, he will shortly move into the top 40 greatest scorers in United's history.
Newcastle's first-half showing was woeful as twice the Belgian part-timers were prevented goals by last-gasp tackles.
The first of those chances came on the half-hour mark when Sebastien Siani broke only to be denied by a stunning Titus Bramble challenge.
That was emulated nine minutes later by an equally impressive Steven Taylor tackle after Wouter Vandendriessche went clear on goal.
Newcastle had enjoyed a bright enough start before fading away after failing to add to their first leg lead.
As early as the fourth minute, Stijn Meert popped up on the line to keep out a Taylor header from Solano's corner.
A flowing move then ended with James Milner driving over and after 22 minutes a ferocious Kieron Dyer shot from 30 yards was only gathered by Sammy Bossut at the second time of asking.
Martins had a good chance early in the second half, but directed his header wide from Damien Duff's cross.
SV had a great chance to take the lead after 58 minutes when Bart Buysse was presented with a free back-post header but directed his effort wide.
Martins pounced to settle the issue with a delightful finish after 68 minutes. Put clear by Duff he beat Bossut to the ball and nonchalantly chipped it over the keeper for his fourth UEFA Cup goal in this campaign.
Substitute Andrew Carroll almost got on the scoresheet when his charge down from a Bossut clearance flew just wide.
Manager Glenn Roeder asked for a win and a clean sheet and got exactly what he wanted.