Markey led in all three by 15 percentage points or more, and more than doubled Lynch's portion of the vote in Sandwich.
That result echoes other recent polls of the race that have shown Markey leading Lynch by a double-digit margin.
But Lynch released internal polling that showed him only 6 percentage points behind Markey, and some Democrats in the state say the underdog has picked up steam since the Boston Marathon bombing. His campaign told the Boston Globe that he's expecting 23 percent turnout and a 5-percentage-point margin in his favor.
"We are very confident in our GOTV operation, and based on the energy and enthusiasm of our supporters, we are expecting a strong turnout tomorrow," said Conor Yunits, a spokesman for Lynch.
The Republican field is significantly tighter, with former ATF acting director Michael Sullivan slightly leading local businessman Gabriel Gomez in Boston, while Gomez doubles Sullivan's vote margin in Shrewsbury, the two Massachusetts towns chosen as bellwethers for the Republican field.
When voters leaning towards one candidate were added in Boston, Gomez and Sullivan both take 41 percent of the vote.
The survey was conducted for Suffolk University and 7 News from April 25-28 among voters most likely to vote in the primary, and has a 5.65 point margin of error.