The on-loan Blackburn striker struck twice in Tuesday night's Championship clash at a rain-lashed Home Park to take his recent run to four in three games to ease the Pilgrims' relegation worries.
Victory also marked Sturrock's 100th win in his two spells as Argyle boss but his more immediate concern will be adding to the Greens' three match unbeaten streak.
Sturrock said: "Galls is a quality player. I think that's 11 goals he's got for the season and with the goals comes confidence.
"You saw that out there, but what really pleased me is when Watford got it back to 1-1, we showed the character to go on and win the game.
"That may not have happened a few weeks ago."
Argyle followed up their first win of 2009, 1-0 at leaders Wolves on Saturday, with their first home win of the year.
The Scot added: "It's been long overdue but I think we were worth it tonight. I did not think we played as well in the second half but you have to give credit to Watford, they improved in the second half.
"Now we have got a biggie at home to Reading on Saturday, and they won tonight and the teams down with us - like Southampton and Norwich - have won so there's still plenty to play for and I won't be happy until we are past the 50-point mark by some way."
Watford boss Brendan Rodgers made five changes to his winning line-up following Saturday's 2-0 success at Crystal Palace, their third win on the trot.
Rodgers said: "I am disappointed with the result.
"We made two mistakes tonight and to be fair they are probably the first mistakes we have made in about five games.
"I was happy with the second half, with their character and it was a terrific goal by Tommy Smith.
"We went on the front foot then.
"As I said, we made two mistakes and got punished tonight, so congratulations to Plymouth.
"I made some changes tonight. I just feel that we have got a load of games coming up and the idea was to give Tommy and a few of the others a rest tonight but know the group was still strong and allows to keep the intensity going.
"Tommy came on and he was great and scored an excellent goal.
"I trust the players, we just never got going first half and didn't get high enough up the pitch and I thought Plymouth played well first half."
Gallagher's 35th-minute penalty opener came after recalled winger Alan Judge, also on loan from Blackburn, had his solo run down the left cut short by Gavin Hoyte.
Smith - on as a half-time replacement for Will Hoskins - went solo for his 14th of the season, angled home from the left following a superb run.
Argyle countered when Sturrock switched Jamie Mackie to the centre and Gallagher out to the left wing in the 72nd minute.
Immediately Mackie's incisive run down the middle led to Plymouth's winner as Judge squared the ball back across the penalty area and Gallagher swooped to side foot home from 12 yards.