A Harvard Medical School study suggests that changing the way doctors are paid could narrow some of the health disparities between poorer and wealthier patients.

Poverty has long been linked to poorer health, an intractable problem that health care experts have long sought to address. The study suggests that one solution may lie in the way health care providers are compensated by insurers.

The paper, published Monday in the journal Health Affairs, studied one type of coverage offered by Blue Cross Blue Shield of Massachusetts. The contract links what physicians are paid to dozens of health care quality measures. When patients score high on those measures and doctors stay under budget, they earn more money.

The study found that quality for all patients in the Blue Cross contract improved, but the gains were greater for poorer patients. The findings appear to be the first of their kind in health policy.

The improvement largely was in access to care, such as medical checkups, cancer screenings, and blood pressure checks. Experts believe this type of preventive care can help avoid difficult and costly health problems down the road.

“Longstanding disparities in health care quality and health outcomes for poorer patients — we saw those disparities close,’’ said Dana Gelb Safran, senior vice president of performance measurement and improvement at Blue Cross, the largest commercial health insurer in the state. Safran worked with Harvard researchers on the study.

The findings, though limited to members of just one insurer, suggest that the way payments are structured has the potential to improve the health of those who need care the most. That is a promising sign as other health insurers, Medicare, and Medicaid continue to the move to so-called alternative or accountable care models, which tie payments to budgets and quality scores.

“This is an important finding,’’ said Dr. Mark Friedberg, senior natural scientist at the Boston office of RAND Corp., a research organization.

“It’s been really hard to put a dent in disparities, and that’s not for lack of trying. It’s a really important and really difficult problem.’’

Friedberg was not involved with the study.

Blue Cross was the first Massachusetts insurer to shift its payment model, with the launch of what is called the Alternative­ Quality Contract in 2009. The contract has grown to include roughly 800,000 people, most of them in health maintenance organizations, or HMOs, and some in preferred provider organizations, or PPOs.

Pushed by state and federal laws, other insurers have rolled out similar payment models, as has Medicare, the government program for seniors.

The Massachusetts Medicaid program, which serves low-income families and individuals, is scheduled to move to accountable care models later this year.

These payment models require doctors to better manage care by reminding patients to get regular checkups and screenings, and in some cases deploying care managers to closely track the health of people with chronic illnesses.

The goal is to change incentives so doctors are paid more when they help keep patients healthy and out of hospitals — not when they perform extra services and procedures.

New payment models, by better coordinating services and cutting waste, are also seen as critical to controlling rising health care costs nationwide. But studies have shown only modest savings so far.

The change in health care payments has not been free of controversy.

Some doctors question whether insurance contracts are tracking the right measures. Some health policy experts worry that new payment models could worsen health outcomes by encouraging doctors to skimp on necessary care.

But this paper suggests the opposite, said Dr. J. Michael McWilliams, an associate professor at Harvard Medical School who was not involved with the study.

“This is very reassuring evidence and certainly supports the use of alternative payment models,’’ he said.

The study looked at about 299,000 Blue Cross members who lived in poorer neighborhoods across Massachusetts and about 244,000 people from more affluent neighborhoods.

It tracked how many met Blue Cross’s quality measures over five years. Between 2007 and 2012, poorer patients improved more than wealthier patients according to one important set of quality measures.

In another set of measures, poorer and richer patients saw roughly equal improvement.

Blue Cross’s 64 quality measures track qualities such as how well patients manage chronic illnesses, how often they are screened for cancer, and whether their blood pressure and cholesterol levels are on target.

Several health experts, while encouraged by the study, said the details of health insurance contracts vary, so progress for these Blue Cross members may not necessarily be replicated among members of other commercial and public health plans.

“It is one piece of evidence,’’ said Dr. Zirui Song, a resident physician at Massachusetts General Hospital and lead author of the paper. “It also motivates further study.’’

Dr. Sandro Galea, dean at Boston University’s School of Public Health, said the paper points to the benefits of shifting away from the fee-for-service model of paying for health care.

“It provides fuel to the fire,’’ he said, “that these approaches have real potential in helping improve the health of marginalized populations, and in so doing narrow health gaps between health haves and health have-nots.’’

Priyanka Dayal McCluskey can be reached at priyanka.mccluskey@globe.com. Follow her on Twitter @priyanka_dayal.