Ulster started brightly despite playing into a strong breeze and were 3-0 up inside four minutes courtesy of a well-struck penalty from Paddy Jackson.
Two minutes later, hooker John Burns scored the first try of the game after an excellent midfield break by Farrell. The conversion was missed by Jackson.
In the 21st minute Craig Gilroy, who burst onto the scene last season, added a second try for the visitors with a clinical finish. Neath responded with a penalty shortly afterwards to reduce the arrears to 13-3.
Ulster continued to dominate affairs up front and number 8 Robbie Diack was rewarded for an industrious first half with a try just before the break. Jackson was this time able to add the extras.
Neath started the second half with a bang and crossed the whitewash within three minutes of the restart. Diack was shown a yellow card a minute later and the Welsh side capitalised immediately with another try, which was converted.
The next half hour was a tense affair with both teams putting in magnificent defensive performances. There were limited scoring opportunities and neither side was able to score until three minutes from the end.
It was replacement scrum half Blane McIlroy who made the game safe for Ulster as he scored a debut try. Fellow newcomer Nelson then scored a fifth try right at the death to complete an encouraging 34-15 win.
Expressing his satisfaction with the performance afterwards, McLaughlin said: "I'm pleased with the effort from everybody, the young guys and the older hands did really well. They fought hard together and we came away with a very impressive win.
"Chris Farrell, Peter Nelson, Stuart Olding and a few others were starting in a senior Ulster jersey for the first time and were a credit to themselves. They did an outstanding job for us.
"The more experienced players deserve praise too because they encouraged and helped the younger players. I thought Lewis Stevenson did very well for us as captain tonight."
He continued: "In the first half, the quality and tempo of our play was outstanding. In the second half we had to dig deep. Neath came at us exceptionally hard, just like they did when they played the Ravens at Shaw's Bridge last season.
"All credit to us, we leaked two tries early in the second half but we came back strongly and scored two excellent tries at the end to complete the game."
McLaughlin believes his side are shaping up nicely ahead of the RaboDirect PRO12 opener against Glasgow Warriors on Friday, September 2.
"We are looking forward to our next friendly against Harlequins next week and can take confidence from this performance," he admitted.
"The tempo we played at tonight and the courage we showed in the second half will certainly stand us in good stead next week and for the season ahead."
ULSTER: Peter Nelson; Michael Allen, Christopher Farrell, Luke Marshall, Craig Gilroy; Paddy Jackson, Ian Porter; Paddy McAllister, John Burns, Jerry Cronin, Lewis Stevenson (capt), Neil McComb, Mike McComish, Willie Faloon, Robbie Diack.
Replacements: Andrew Warwick, Callum Black, Adam Macklin, James Simpson, Ali Birch, Blane McIlroy, Stuart Olding, Conor Gaston.