Carter had also been top scorer against Uganda – her second half century in four innings on Scotland’s current tour.
“Darcey’s just done brilliantly well,” Bryce said. “Hopefully she can keep it going, because it’s great to see someone so young doing so well.
“I think we’ve been exceptional at the back-end with the ball, so credit to our bowlers for sticking at it in those tough situation.
“I think that’s great to see. When the pressure’s on, they’ve really stood up and that’s been really important.”
Carter’s 76, during which she found the boundary 10 times, was a career-best in T20 international cricket.
She had a 70-run stand with Watson for the second wicket before before Scotland added 51 from the final five overs, Chatterji adding an 11-ball 19.
In reply, Saum Mtae and Fatuma Kibasu had a 50-run opening partnership inside six overs.
However, Carter struck twice in the same over, bowling Mtae for 27 before Neema Pius was caught behind for a duck to put Tanzania on 58-2 before catching Kibasu for 28 on the boundary from Niamh Robertson-Jack’s delivery.
Tanzania were 86 behind at the halfway stage, but Hudaa Omary and Jenipher Kimaro added 54 in just 33 deliveries.
However, Scotland then took five wickets for 16 runs in 22 deliveries to secure victory.
Scotland next face United Arab Emirates on Sunday.