Conte's side went 2-0 up after 18 minutes through an Adam Smith own-goal and an Eden Hazard strike before conceding a goal to Bournemouth's Joshua King.
In the second half, Spanish defender Marco Alonso scored in the 68 minute from an wonderful free kick to solidify Chelsea's lead.
Leaders Chelsea maintained their seven-point cushion over Tottenham in all the style befitting champions-elect and now need at the most 15 points from seven matches to seal the silverware.
The win left Chelsea seven points clear at the top of the table as they chase the title in Conte's first season at the club.
"The most important thing is on the pitch", Conte said after Chelsea won 3-1 at Bournemouth to stay on track to win the title in the Italian's first season in charge. "To become a great season and to write history you must win". For sure there was something, but I think it's right also to accept the decision of the referee.
"I am very happy for this experience because for me and my family it is incredible", he said.
"When you have this type of opponent (Tottenham) who is in good form and wants to catch you, it is important to have a good answer".
Former Italy boss Conte insisted he relishes the intense pressure surrounding Chelsea's tilt for the title - and even admitted he would crank up the heat on his players himself if necessary.
There is a chance that the Blues can win the double this season - they face Tottenham Hotspur in the semi-finals of the FA Cup later this month. Costa poorly sliced his shot - it looked to be going closer to the corner flag than goal - but the ball spun off the backside of Smith and trickled in off Artur Boruc's far post. "We know what we are playing for, the motivation is 100 percent and we played a good game".
"At this moment, Diego is not scoring, but he's totally involved in the team and our football".
However, Antonio Conte's side eased past the Cherries, registering a 3-1 victory at the Vitality Stadium, with Marcos Alonso netting a cracking free-kick.
"Chelsea are an outstanding team and their system works very well for them", said Howe. "We Shall Not Be Moved" has been covered by the likes of Mavis Staples, Johnny Cash, and now the faithful Chelsea fans who were loud as ever on Saturday.
"The team deserve full credit because the energy and the way they played was fantastic".