The infamously feisty Costa, dropped in January after reports of a row with Chelsea boss Conte, was left walking a disciplinary tightrope after being booked for simulation in the 16th minute of the game at the Bet365 Stadium.
Mark Hughes feels hard done by Chelsea's late victor, saying Stoke's play was deserving of a share of the points on the day.
21 Antonio Conte has set Chelsea a target of winning 21 points from the 30 remaining to bring the Premier League title back to Stamford Bridge.
The controversial Spain striker was involved in numerous clashes with Stoke players, particularly centre backs Ryan Shawcross and Bruno Martins Indi, but managed to stay on the pitch and Conte praised the way Costa refused to be baited.
"We didn't do that", he said. "But he's important for the club and I think the club knows that, so they will do whatever to have a happy ending. No quarter given or asked". Having started the weekend with a 10-point lead at the EPL summit, the Blues were on course for a share of the spoils against the Potters once Willian's free kick was cancelled out by Jonathan Walters' penalty before half-time.
Conte had Cahill to thank after the defender fired home the victor in the 87th minute, as Chelsea left it late to clinch all three precious points.
"The attitude and level of performance was really good. For this reason, we won today", said the Italian.
'One of the biggest clichés in the game is that you do not win titles without a rock-solid defence, ' Nevin wrote in his Chelseafc.com column. There are 10 games to go, today was a great win, a good signal, but it is important to continue with the same commitment and work rate as a team.
Chelsea are a shoo-in for the title and could win the FA Cup as well in his debut campaign. "We have to look at ourselves. Today we were ready".