The Linnets almost made a late comeback, although it would have been hardly deserved.
Lynn were 3-0 down with ten minutes to go before Dean West's first goal for the club and a scorching Adam Smith strike made it interesting.
A draw would have been an injustice on the home side, who counter-attacked effectively. Lynn are clearly missing the defensive solidity of Grant Cooper, without whom they have conceded seven goals in two games.
Lynn were also without Sam McMahon, who fell ill on Friday, keeper John Higgs and midfielder Cedric Anselin. Aaron Benstead, signed back with the club as a replacement for Higgs, generally did well, although he was at fault for one goal.
When Linnets manager Tommy Taylor was asked whether it was the case of a bad day at the office, or down to the players who were missing, he said: "It was a bit of both. It helps when you've got those players. Everybody's been playing together for a long time, and we had seven clean sheets in 12 games.
Taylor added: "Sam and Cedric were not in midfield, and we didn't get anything coming from midfield.
"The first two goals were bad defending, the third was our free-kick, and they broke away and scored."
"We got back in the game with two goals, and had enough chances, but on the day they were a very good team. When we went to 4-4-2 it was a different game."
On substitutes Matty Peters, who made his first senior league appearance, and Luke Fell, Taylor added: "They played well and brightened the game up."
The Bluebells were two goals ahead in 20 minutes. After a quarter of an hour, a Lynn attack broke down and Yate flew down the left, slicing through The Walks outfit's defence which resulted in Adam Sims firing home.
At the other end the Linnets won a corner which was cleared to midfielder Matt O'Halloran, whose first-time effort hit a defender from five yards and was cleared.
Yate on 20 minutes doubled the advantage, another quick break was switched across field which prompted Benstead to rush out and bring down Darren Edwards just outside the Lynn penalty area. With Lynn defenders covering, the referee opted for a yellow card, not red.
David Elsey hit the resulting free-kick around the wall, Benstead palmed it up but it looped into the net.
Elsey could have received his marching orders when tangling and striking out at O'Halloran on the halfway line, but Mr Farries took no action other than giving Lynn a free-kick.
Benstead reprieved himself with a string of saves, denying Edwards who was clear in the box and then a minute before half-time diving to his left to thwart Justin Pritchard.
However, Pritchard it was who scored Yate's easy third goal on 52 minutes, with Sims the provider when another quick counter saw just West left on his own in defence.
Benstead then made two good saves in the next ten minutes, from Steve Campbell and Jason Wood, whereupon Yate sat back.
Meanwhile, the introduction of Peters and Fell gee'd up Lynn.
West had scrambled an effort off the line, but got his name on the score sheet after 80 minutes, heading home a Smith corner from the right.
On 88 minutes Peters fed Smith, who sent into the net a cracking 30 yard left-foot shot, with home keeper Tony Court nowhere near.
In injury time Smith nearly earned a draw with a similar effort, this time Court got just enough on it to palm it over the bar.
Yate: Court, Sims, Elsey, Brice, Jefferies, Vickerman, Wood, Chenoweth, Edwards, Pritchard (Cox 70), Campbell. Subs not used: Metheringham, Wyatt, Sylvester, Bridson.
Lynn: Benstead, West, Smith, Hammond (Harvey 30), Jones (Fell 65), Camm, Defty, Carey, Nolan, Bloomfield, O'Halloran (Peters 65). Booked: Benstead 20.
Referee: J. Farries (Adderbury, Oxfordshire).