The altar call predates Billy Sunday, though possibly not by that name.
Charles Finney pioneered many evangelistic methods in the 1820s and 1830s, including what he called the "anxious seat" or "anxious bench", where sinners could come forward to receive instruction and counseling.
William and Catherine Booth, founders of the Salvation Army, used similar techniques—although they renamed the "anxious seat" to the "mercy seat". Like Finney, the Booths considered the altar call to be just the first step toward salvation.
Sometimes people would stay there all night, and on a few occasions, even a few days, weeping and confessing their sins with broken hearts. There were always some who would stay right there to instruct them further, encouraging them to make a clean sweep of sin from their lives.
Dwight Moody began having altar calls after the Great Chicago Fire of 1871 killed more than 300 people and destroyed Moody's church building, just after he had preached about repentance.
Moody asked his congregation to evaluate their relationships to Christ and return next week to make their decisions for Him. That crowd never regathered. While Sankey was singing a closing song, the din of fire trucks and church bells scattered them forever, for Chicago was on fire. The Y.M.C.A. building, church, and parsonage were all to be lost in the next 24 hours.
After the fire Moody vowed never to delay in asking his listeners to make a decision for Christ. Moody, however, stressed that the altar call itself did not bring about salvation.
It is not our work to make them believe. That is the work of the Spirit … I cannot convert men; I can only proclaim the Gospel.
However, by insisting that they make an immediate decision, Moody began to blur the line. At least one reporter understands Moody's methods to imply a connection between the altar call and salvation.
Moody was quick to point out that only the Spirit awakens sinners, and the individual’s trip to the altar is simply a sign marking one’s salvation.
So it's fair to say that no preacher prior to Billy Sunday explicitly equated the altar call with salvation, but it's possible that the "immediate decision" that Dwight Moody asked of his listeners could have been understood that way.