The Teessiders have taken seven points from their three Championship games so far, winning on the road at Leeds and Barnsley to take them up to fourth going into the weekend's action.
On Sunday they face Birmingham at the Riverside Stadium, and Mowbray has urged Boro fans to come out in force and create a winning momentum.
"We're scoring goals and winning matches and we have to try to keep it going," Mowbray said.
"If we can continue doing that, hopefully the turnstiles at the Riverside will keep turning and the people will watch the team in numbers and before we know it we've got a really good matchday atmosphere at the Riverside.
"It goes hand in hand - the more people come, the more they enjoy the game, the more we give them something to cheer about and they help the team and we continue to get the wins. The crowds get bigger and you get an upward spiral of success.
"There's nothing magical about it - it's hard work, preparation, organisation and support from the terraces. All those things mixed up together can hopefully give you a winning formula."
Belgium midfielder Faris Haroun goes straight into the Middlesbrough squad after signing a three-year deal on Thursday. Defender Tony McMahon is available after serving a one-game ban but full-back Justin Hoyte remains a doubt after limping off with a recurrence of his thigh strain during the 3-1 win at Barnsley in midweek.
Birmingham arrive on Teesside having been involved in Europa League action on Thursday night, claiming a goalless draw in the away leg of their play-off tie against Portuguese side Nacional.
Keith Fahey, Morgaro Gomis and Scott Dann missed the match in Madeira due to minor knocks, although midfielder Fahey was able to take his place on the substitutes' bench.
The attacking trio of Cameron Jerome (heel), Marlon King (knee) and Nikola Zigic (groin) failed to even fly out to Madeira and are yet to feature at all this season. Jordon Mutch will definitely miss out at the Riverside Stadium due to the ankle injury he picked up in training earlier this week.