In the only other top-flight game to survive the Arctic weather, managerless Blackburn Rovers drew 1-1 at home with bottom club West Ham United.
Heavy snowfall and sub-zero temperatures put paid to the rest of Saturday and Sunday's games, including the Stamford Bridge showdown between champions Chelsea and league leaders Manchester United.
United have 34 points to the 32 of Arsenal and Manchester City, who will go top if they beat Everton at home on Monday.
Chelsea have 31 points with Tottenham Hotspur and Sunderland both on 27. Bolton slip to seventh on 26.
Sunderland, along with Manchester United the only teams with an unbeaten home record, have now won five and drawn four of their nine games at the Stadium of Light.
They got their goal on Saturday after 32 minutes when Darren Bent did well to control a deep cross and after his shot was parried by Jussi Jaaskelainen Danny Welbeck threw himself at the rebound to head his fifth goal in six games.
Sunderland had Craig Gordon to thank for keeping them ahead when their goalkeeper brought back memories of one of the club's most famous moments - Jim Montgomery's amazing save in the 1973 FA Cup final upset win over Leeds United.
After a corner was nodded back across the six-yard box Zat Knight shot goalwards from point-blank range only for Gordon to somehow get a hand to the ball, which was almost past him, and divert it up and over the bar.
Bolton pressed hard for the equaliser in the second half and Ivan Klasnic had two great chances in the dying moments but failed to connect properly on both occasions.
"If at the start of the season you'd offered me sixth place at Christmas I would have been pretty happy to take it," said Sunderland manager Steve Bruce, who was forced to apologise to the club's fans following a 5-1 thrashing by local rivals Newcastle United two months ago.
"We have a bit of spirit, some hard work and we have some good players too."
Blackburn, who sacked manager Sam Allardyce on Monday, led at Ewood Park with a scrambled effort by Ryan Nelson early in the second half.
West Ham, so hard-hit by injuries that they had to give a debut to fourth-choice goalkeeper Ruud Boffin, earned a desperately-needed point through Junior Stanislas 12 minutes from time to ease the pressure on manager Avram Grant for a few days at least.
