Paul Lambert's men have already brushed off their Championshipstruggles twice in 2017 by grabbing shock away victories at Stoke City and then, most sensationally, Liverpool. The match was quite even until just after the hour mark where a cross from Willian was met at the back post by Pedro.
That is a target for Conte, who says nothing can be taken for granted after the Imps' win at Burnley saw a non-League side advance to the last eight for the first time in 103 years.
Chelsea will look to avoid an FA Cup upset at Wolverhampton Wanderers on Saturday with the mood still upbeat despite being held to a disappointing 1-1 draw at Burnley last Sunday.
In the second period Costa turned Batth inside out but slammed his shot into the side netting, and soon after there was a glare for refereeJon Moss for failing to spot the central defender hauling him down off the ball as Chelsea countered.
Numerous players in Chelsea's squad against Wolves were part of the team that lost to Bradford City in the fourth-round two seasons ago.
It was a Jack Price cross from that flank that Kurt Zouma was unable to connect with, allowing the ball to drop for Saville. It landed at the feet of Saville 12 yards out, and though he caught it well it clattered off the frame of the goal. The England Under-21 global will play as the midfield anchor thus providing Fabregas with the chance to showcase his creativity versus the Wolves. The appeal was dismissed.
The Blues are going through a stupor at this point, having won just one of their last four away games in all competitions.
Diego Costa did meet a Victor Moses cross soon afterwards, but his back was to goal and he could only direct the ball over. From there, the Blues dominated and Diego Costa added a scrappy second in the 90th minute.
The difficulties of fighting on many fronts were made clear again for Arsenal and Tottenham this week - catastrophically so for the Gunners - and served to emphasise that a key factor in Chelsea's rise back to the top has been their relatively straightforward fixture list. A defence splitting pass from Fabregas found Diego Costa.
Antonio Conte's side took over in the second 45 minutes, with an opportunity for Costa before Pedro opened the scoring in the 65th minute.
DF Cesar Azpilicueta, NR - Replaced Pedro in the 73rd minute and immediately shored up the left flank.