Watkins' opening goal just before the break, Lynn's 100th in the competition, set The Walks outfit on the way and only some fine keeping from Basingstoke's Scott Tarr and the woodwork denied the Linnets an even bigger winning margin.
The Linnets had to survive a couple of late scares, with Steve Wilson having a nervous time between the posts in his 100th game for the club.
"We were well worth the win," said joint caretaker boss Kevin Boon.
"Basingstoke play good football in a higher league, and we more than matched them. It's a good benchmark for our lads. If we continue to progress, I don't think we'd have a problem playing regularly in that company.
"It was the type of match when we needed to be strong defensively, particularly when Mark Burrows had to go off. Gary Setchell moved inside and showed why he was playing in the Conference this season. And Jamie March made two tremendous blocks when he came on."
Joint caretaker boss Darren Bloodworth said: "We weren't as slick as we have been recently, but we were up against a side from a higher league.
"I thought we still played a lot of good stuff and dictated the game for long periods."
Lynn swarmed forward at every opportunity and in the 7th minute David Staff saw one of his curling free-kicks cannon off the woodwork after a foul on Jack Defty.
Three minutes later Paul Raynor's lofted centre found the head of Mark Burrows, but his effort deflected off a Basingstoke defender and came back off the post.
That was Burrows' last involvement as he limped off with a hamstring injury, but Gary Setchell showed his versatility by slotting into the centre back role with ease, while Jamie March enjoyed one of his best games after coming on to deputise for Setchell at left back.
Lynn continued to dominate, Adam Jones twice trying his luck from long range, while the lively Staff shot wide and Defty's pullback wasn't converted.
Basingstoke were more than a threat going forward and in the 30th minute Wilson got the faintest of touches to a Neville Roach strike and Carl Holmes cleared off the line from the resulting corner.
The deadlock was finally broken four minutes before the break when Raynor's pass was finely controlled by Watkins, who rounded Tarr before tucking the ball home.
Lynn camped in the Basingstoke half for the opening 20 minutes of the second period, with the hard working Mark Camm again showing his ability to cover ground all over the pitch.
The midfield dynamo exchanged passes with Carl Holmes before drilling wide, while Save forced Tarr into a fine save to his right.
Watkins, struggling with a thigh injury, was withdrawn, but Lynn's attacking instincts were resumed with the introduction of Robbie Harris, who gave the Basingstoke defence another headache with his pace.
The youngster teed up Staff to shoot wide midway through the half, before a goalline clearance from March denied Basingstoke's Ben Surey a certain equaliser soon after.
March's fantastic clearance proved to be even more valuable when Staff picked up a ricochet from Holmes to supply a cool finish for Lynn's second in the 76th minute.
Wilson then flapped at a Basingstoke corner and Jason Bristow pulled a goal back in the 85th minute and leading Stoke's scorer Craig McAllister heading wide as the visitors upped the pace in the final exchanges.
But Lynn held firm to break forward and add a third through Harris, whose back heel was only half saved by Tarr before the striker made no mistake with the rebound.
There was still time for March to acrobatically head off the line from Roach but a Basingstoke second would have been rough justice on Lynn for yet another superb display.
Lynn: Wilson, Jones, Setchell, Burrows (March 16), Fuff, Raynor, Defty, Holmes, Staff, Watkins (Harris 65), Camm. Subs not used: Woodrow, Bacon, Nobes.
Goals: Watkins (41), Staff (76), Harris (89).
Basingstoke: S. Tarr, Nathan Stamp, Neville Stamp (I. Dickens 9, A. Ewin 68), R. Kember, J. Bristow, R. Allaway, B. Surey, E. Elad, C. McAllister, N. Roach, O. Burgess (B. Elmore 73). Not used: D. Wyatt, S. Hemmings.
Goal: Bristow (85).
Referee: R. Burton (Northants).