Adjusted revenue from equities sales and trading rose 33 percent to $2.27 billion, meaning that Morgan Stanley lost its lead in the business over Goldman Sachs, which reported revenue of $2.32 billion for the quarter.
Global stocks have generally performed strongly since the start of the year, with several indexes at or close to record highs as a number of central banks have eased monetary policy.
Revenue in the bank's wealth management business rose 6.2 percent to $3.83 billion, accounting for 39 percent of total revenue.
Excluding special items, revenue from trading fixed-income securities, currencies and commodities (FICC) rose 15 percent in to $1.90 billion.
Morgan Stanley, the last big U.S. bank to report for the quarter, is focusing less on bond markets and more on managing money for the rich as a way to free up capital and comply with stricter regulatory requirements since the financial crisis.
The wealth unit's contribution to revenue jumped to nearly 45 percent last year from less than 20 percent in 2006.
In the same period, FICC revenue fell to about 12 percent of overall revenue from more than a third.
The bank's FICC business, like those of its rivals, got a boost in the quarter after the Swiss central bank scrapped a cap on the franc, the European Central Bank announced its quantitative easing program and the U.S. Federal Reserve moved to tighten monetary policy.
"This was our strongest quarter in many years with improved performance across most areas of the firm," Chief Executive James Gorman said in a statement
Morgan Stanley's stock has been underperforming when compared to fellow banking giants Goldman Sachs and JPMorgan Chase.
Last week, both Goldman and JPMorgan reported first-quarter earnings per share that topped analysts' expectations.
Goldman, helped by a burst of trading activity in January when the Swiss central bank removed a cap on the franc, saw profits rise to $5.94 per share, while JPMorgan delivered profits of $1.45 per share.
Last January, Morgan Stanley reported a drop in fourth-quarter adjusted earnings.
—CNBC's Terri Cullen and Reuters contributed to this report.