The market analysis firm revealed that between September and October, both Google and Bing inched ahead. The increases were far from dramatic but at least they saw increases.
According to ComScore, Bing's share rose from from 9.4 percent to 9.9 percent. At the same time, Google saw a share bump, moving from 64.9 percent to 65.4 percent. Analysts also confirmed that Google in October saw a 17.4 percent year-over-year increase.
Yahoo, which remains in second place between market leader Google and third-place Bing, didn't have such a strong month.
Yahoo saw its share slip, slipping from 18.8 percent in September to 18 percent last month, according to ComScore.
Ezra Gottheil, an analyst with Technology Business Research, said Google, with steady control of more than 60 percent of market share, is such a force to be reckoned with that Bing is doing well to make even modest headway.
"Bing has established a position that is, for now, stable.If Bing innovates effectively, it can move forward. It's in a not bad position, considering Google's momentum, but there's nothing happening now to show that it can take share from Google," said Gottheil.
"With Google, it's not so much about growth any more, but the large number of people for whom Google is the search engine. Google is an ocean liner. It's going to take a lot of effort and a lot time to slow it down."
When it comes to Yahoo, Gottheil said the company's search presence is on a downhill slide that could become hard to control.
"Yahoo's search engine now is a lame duck," he added.
"Yahoo has been on a long-term decline. The battle between Bing and Google raises awareness about search engine capabilities, and may drive some users to try other products, but basically, Yahoo has not given its search engine users a good reason to stay."
In September, ComScore reported that Bing increased its share of the competitive market by 4.5 percent between July and August. The new search engine held a 9.3 percent share of the market at the end of August.
Also that month, ComScore noted that Google had slipped 0.1 percent to hold 64.6 percent of the market at the end of August.