Teenager Ashley Barnes, strike partner Jamie Mackie, on-loan Blackburn winger Alan Judge and central defender Marcel Seip were all on target to put the Pilgrims 4-0 ahead after 37 minutes.
And Sturrock said: "I knew we had something like this in us. We have had our home games where we have hit bars and posts, had goals disallowed.
"Something that I did not expect was to be 4-0 up at half-time. We have got a home game plan and the boys have worked very hard at it.
"I think we showed in our last home game against Burnley signs of what we can do, even though we did not get a result
"Today all their hard work and endeavour paid off. They won at Blackpool, which was an important result for us, and now - with two home games come in the last four - we have got an important home win."
Barnes, 19, got the ball rolling when he headed home full-back Gary Sawyer's cross from the byline in the 14th minute after City failed to clear Paul Gallagher's free-kick from wide on the left.
After claiming his first Argyle goal, Barnes then sent an overhead kick into the path of Mackie to make it 2-0 in the 26th minute.
With City still reeling, Judge exchanged passes with Gallagher and swept in from the left before unleashing an unstoppable 18-yard drive into the top corner.
City threatened a brief comeback but Argyle goalkeeper Romain Larrieu made a brilliant diving save to keep out substitute Kevin Thornton's angled drive.
Argyle countered by winning a corner, Gallagher took it and Chris Barker headed the ball on at the near post for Seip to swoop to convert from close range.
Judge so nearly made it 5-0 in the 40th minute, meeting Larrieu's long free-kick with a volley that flew inches over.
Larrieu flapped a Daniel Fox free-kick over as half-time approached but fuming City boss Chris Coleman admitted: "I was embarrassed in the first half.
"I'd like to apologise to the supporters for making the trip down to Plymouth, taking time off over the Easter weekend to watch that nonsense.
"Forget the second half. How many times have a team been 4-0 or 3-0 down at half-time and there's no goals in the second half?
"The game was done, it was over at half-time. It was an unacceptable performance in the first half.
"I am not happy about losing 4-0 or the fashion we conceded the goals."