The Teessiders have taken an impressive 31 from a possible 39 Championship points to date at the Riverside Stadium, a vast improvement on the last campaign, when they drew no fewer than 10 matches on their own pitch.
That has helped them to maintain their push for the top two, but Mowbray knows there is no room for any let-up as they prepare to welcome Watford on Saturday.
He told the club's official website: "We have won 31 points out of 39 at home and we have to maintain that points haul.
"We are only two points off an automatic promotion place and it's important we keep on track.
"If anything, we have to be better in the second half of the season than in the first to hit the top two."
Mowbray is targeting a sixth successive home victory this weekend against a Watford side currently seven points and two positions behind with a game in hand.
Mowbray said: "They are going to be a threat. I studied them this week and they can score goals and are very hard to break down.
"They have won six away games, including big victories at Leeds, Sheffield Wednesday and Brighton, and they have some clever, creative players.
"Some people might argue it's more important not to lose to a team just behind us, but I think it's important to try to win.
"It would be a huge victory for us that would really keep them at arm's length and establish a real gap."