The two Premier League sides may be more concerned with top-flight survival than enjoying a cup run this season but they should have been able to serve up better fare than what they offered at the Stadium of Light.
For the best part of an hour play was littered with mistakes, mis-placed passes and hopeful balls into no-man's land.
Jones finally produced a moment of quality with a 57th-minute header which was surpassed only by Cisse's volley 10 minutes later.
Substitute's Ebi Smolarek's ballooned cross-cum-shot caught out goalkeeper Martin Fulop but the Black Cats hung on to give manager Ricky Sbragia victory in his first home match since taking the job on a permanent basis.
The opening exchanges were untidy with neither side able to carve out any real chances.
It took until the 15th minute before either team had a sight of goal and when they did Jones scuffed his shot wide having been put in on the right by Kieran Richardson's throughball.
However, chances were few and far between as too often blind passes were played straight to opponents, with Bolton in particular pumping long balls at the Sunderland defence rather than a team-mate.
In the 20th minute Carlos Edwards was given space to run into but with time to make a telling cross he drilled the ball into the near post and the danger was cleared.
Sunderland won their first corner in the 23rd minute but when El Hadji Diouf's inswinging cross came through a crowd of players Ricardo Gardner was on hand to clear off the line.
Just before the half-hour mark Johan Elmander shot weakly at Fulop having been put through by Fabrice Muamba, which typified the way the game had gone.
Muamba was booked for a foul on Diouf, linked with a move to Blackburn, in the 32nd minute.
If he was due to leave soon at least the Senegal forward was putting himself about against his former club.
Right-back Pascal Chimbonda, another who could be offloaded by Sbragia this month, spent most of the half complaining to his team-mates and generally looking disinterested.
A further example of the lack of quality on show came when Cisse latched on to Danny Collins' through-ball but poked wide from the left of the penalty area with only goalkeeper Jussi Jaaskelainen to beat.
Late in the half Matthew Taylor's 35-yard free-kick was saved low to his left by Fulop.
The start of the second half was not much better, with Dean Whitehead booked for diving just outside the Bolton box, much to the disgust of the home crowd who were expecting a free-kick.
Jlloyd Samuel's foul on Edwards moments later earned the Bolton defender a yellow card and gave Richardson a sight of goal 25 yards out.
The former Manchester United midfielder drilled his shot into the near post and won a corner, which Jones headed down and Gardner, for the second time in the match, cleared off the goalline.
Gretar Steinsson was booked for fouling Diouf wide on the left in the 57th minute and it proved costly for the visitors.
Richardson swung the ball in left-footed and when Jones met it with his head this time there was no-one to deny him on the line.
Just before the hour mark Kevin Nolan was booked for pulling back Edwards as Sunderland started to get the upper hand.
Edwards then fired an 18-yard shot off the top of the crossbar after a neat passing exchange - assisted by poor Bolton defending - between Richardson and Jones.
But in the 67th minute Cisse doubled the lead when he volleyed home Edwards' right-wing cross.
Richardson limped off in the 76th minute to be replaced by Teemu Tainio before, out of nowhere, Bolton got themselves back in the match three minutes later.
Substitute Smolarek, on for Kevin Davies, found himself in space wide on the right and his looping cross-cum-shot caught out Fulop as it dropped over the goalkeeper and inside the far post.
It sent up a frantic finish but Sunderland held on.
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