Two goals in each half secured a third successive victory for Graham Drury's side who now move up into fifth place in the league standings.
They are also just three points off the second automatic promotion place after keeping a third consecutive clean sheet against a visiting Shropshire side who were forced to field a number of their reserve team players following the resignation of manager Carl Abbott this week.
Daniels boss Drury praised his side for their professional approach to the contest as goals from Brad Wells, Jordan Smith, Ben George and Sam Hollis maintained Stamford's unbeaten home league record.
Drury said: "We had an opportunity to move to move into the play-off places and we had to make sure we grabbed it.
"All credit to Market Drayton because they worked really hard and we had to be patient, but I believe and trust this group of players. We are very together as a group and made the most of the opportunity.
"It can be hard to keep your focus when you're so dominant, but we were very professional and that's now 10 clean sheets for the season.
"We have only conceded 18 goals in the league this season and, in a division where your goal difference is usually minus unless you're in the top three, that's fantastic.
"We are also spreading the goals about the team and it's great that everyone is chipping in.
"The play-offs are the minimum requirement for this club and, if we don't achieve that, then I haven't done my job."
Stamford were forced to make a couple of changes to their starting line-up with Eliot Putman unavailable while Jon Challinor was ruled out through illness.
They made the most of the early running though against a Drayton side who were content to sit deep and defend in numbers.
Jake Duffy saw an early free-kick gathered at the second attempt by Jay Nash while Wells saw a header collected by the visiting custodian.
Stamford then had a gilt-edged chance to break the deadlock when Smith was bundled over in the box, but the usually-reliable Liam Adams fired the resultant spot kick wide.
Rob Morgan and Mike Armstrong both sent shots just wide of the visitors' goal before Stamford got the breakthrough their pressure deserved seven minutes before half-time.
Wells turned his marker smartly before steering home a tidy finish into the far corner to break Drayton's stubborn resistance.
The relief of scoring the first goal seemed to give Stamford a new lease of life and a stunning passing move opened up the visitors where George fired narrowly wide.
The Daniels doubled their lead right on the stroke of half-time when Duffy's near-post corner was turned home by Smith.
The visitors changed their goalkeeper at half-time with Ash Rawlins entering the fray and he was beaten for the first time just past the hour mark.
Duffy was the architect of the goal as he surged into the box and, although Rawlins blocked his initial effort, George was following up to tap home his second goal in as many games.
The fourth and final Stamford goal followed eight minutes later when a terrific run from Bradley Fortnam-Tomlinson created the opening for substitute Sam Hollis to finish with aplomb.
Dan Haystead had rarely been called into action, but he produced an athletic save to turn away the visitors' best effort from James Tindall-Bennett.
Substitute Harry Peasgood, on for his league debut, nearly capped a memorable first Evo-Stik appearance as he turned another Duffy corner goalwards only to see his effort blocked on the line as Stamford finished, like they started, in the ascendancy.
# | Team | Pl | Pts |
1. | Basford United | 42 | 100 |
2. | Alvechurch | 42 | 85 |
3. | Frickley Athletic | 42 | 82 |
4. | Bedworth United | 42 | 74 |
5. | Chasetown | 42 | 73 |
6. | Stamford | 42 | 71 |
7. | Leek Town | 42 | 68 |