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The Londoners eventually won 2-0 with a fortunate Frank Lampard effort but fully deserved all three points which could have taken them top of the league had Arsenal slipped up against Middlesbrough at Highbury.
The Icelandic striker's fifth league goal of the season was beautifully taken after he ran onto Jimmy Floyd Hasselbaink's slide-rule pass.
It seemed as if Aston Villa goalkeeper Peter Enckelman had his angles worked out but Gudjohnsen managed to produce a low, right footer from the corner of the six-yard box, across the path of Enckelman and the ball went in off the far upright.
The crossbar came to the rescue of the Londoners as early as the first minute when Olof Mellberg's strike seemed destined to give Villa an early boost.
In fact Villa got out of the stalls early and had Chelsea on the back foot for the first 30 minutes, as confirmed by Villa boss Graham Taylor.
"For the first third of the match, it was difficult to see who was third in the league and who wasn't," he said.
"But we lost the plot in the last 15 minutes and the second-half performance was the poorest in six weeks.
"When the second goal went in, our heads went down. The attitude was not what I expect - we never gave Chelsea anything to concern them."
If the first Chelsea goal was well crafted, the second owed much to good fortune.
Lampard collected a throw-in wide on the left in the 57th minute. He angled a cross-shot behind the Villa defence and Gudjohnsen was first to react. He tried to head the ball on, but his mistimed effort confused Enckelman and the ball continued on its curved path into the bottom of the net.
Chelsea boss Claudio Ranieri was not happy with this win: "We did not play well," confessed the Italian.
"But it was important to win. We worked hard but conceded too much space in the first half. We created a lot but the final pass was missing.
"We have to be consistent now. We are second in the league, but it does not matter where we are now, it's where we finish up that is important.
"Last season, at Christmas, we got one point out of five games. That shows how vital it is to do well, at this period of the season.".