Brentford moved up to 13th in the table with 10 points from eight games, while West Ham, booed off by their fans, are 19th with four points.
New West Ham manager Nuno Espirito Santo will have seen the size of the job at hand as his side were second to everything and only the woodwork and wasteful Brentford finishing prevented a rout.
Thiago netted from 10 yards from Kevin Schade’s pass on 43 minutes and Jensen blasted into the roof of the net in added time to seal a victory that Espirito Santo will feel was far too comfortable for Brentford.
“It’s very nice to get the three points and get away from the relegation zone,” Brentford midfielder Mikkel Damsgaard said.
“We missed a lot of chances, on set-pieces we could have had more (goals), but we are happy with the three points. We are finding a rhythm as a team and connecting a bit more.”
Empty West Ham seats
There were empty seats at kickoff as what seemed like several thousand West Ham fans staged a stay-away in protest against chairman David Sullivan and vice-chair Karren Brady.
Brentford came into the game having lost all three of their away league matches this season but had 22 attempts on goal, the most they have managed away from home in the Premier League.
West Ham were over-run in midfield and could not get a foothold in the game, outplayed by a team who had struggled at the start of the campaign.
The goal that had been coming for Brentford arrived just before halftime as a long ball was collected by Kevin Schade on the edge of the box and he held off three defenders before feeding Thiago.
The striker’s shot was half-blocked by West Ham goalkeeper Alphonse Areola, but the ball dribbled into the corner of the net.
It was more of the same in the second half as Brentford dominated possession and Schade struck the crossbar with a header on the hour-mark.
West Ham never looked like finding an equaliser, and Brentford made it 2-0 with virtually the last kick of the game when Jensen was picked out in the box in space and drilled the ball into the net from 15 yards.