There are two questions to consider here. First, there is the practical question of whether Lincoln was able to issue and enforce his suspension of habeas corpus. Second, there is the legal question of whether Lincoln had the express legal authority to suspend habeas corpus. The answers to these questions are slightly different.

Here are the facts: On April 27, 1861, President Lincoln issued an order suspending the writ of habeas corpus in the area between Washington, DC and Philadelphia, an order which mostly effected the state of Maryland. This order allowed federal forces to arrest and detain anyone who was deemed to be interfering with or threatening federal military operations in the area without having to provide a rationale to civilian courts. As you mentioned, Lincoln based his order on Article 1, Section 9, Clause 2, of the US Constitution, which says: "The Privilege of the Writ of Habeas Corpus shall not be suspended, unless when in Cases of Rebellion or Invasion the public Safety may require it." [1] Lincoln argued that this was certainly a case of rebellion and that the public safety required such a drastic measure. Earlier in April, anti-war protesters and Confederate sympathizers had clashed with federal forces in the Baltimore Riot of 1861, and pro-secession elements were pushing for Maryland to secede and join the Confederacy.

Despite some objections to the suspension of habeas corpus in Maryland - including a ruling from Chief Justice Roger Taney (acting as a circuit court judge) that argued that only Congress could suspend habeas corpus [2] - Lincoln enjoyed fairly broad public support for the order. In June 1861, Maryland voters elected a largely Unionist state legislature, and when Lincoln laid out his argument for suspending habeas corpus to Congress in July of that year, they generally supported his use of this power. [3] It is important to note that Congress was not in session at the time that Lincoln issued his order to suspend habeas corpus in Maryland, which raises the question of who has the power to do so if a rebellion or invasion should occur when Congress is not meeting. For Lincoln, the answer was obvious - the President has that power. Although Congress later passed a law expressly granting the President the power to suspend habeas corpus during the "present rebellion", Lincoln insisted that his use of the power was, and always had been, legal. [4]

So, on the practical question - Lincoln definitely have the power to do this. He issued the order, he enforced the order, and neither the Supreme Court or the Congress made a serious effort to stop him. The legal question is a bit murkier. The Constitution does not expressly say that only Congress has the power to suspend habeas corpus, though many (including Chief Justice Taney) argued that the fact that this power is in Article 1 means it is a Congressional power. However, nothing in the Constitution or any other federal law expressly prevented Lincoln from doing what he did, and it is reasonable to assume that the federal government should be able to use this power during a time of rebellion, which the spring of 1861 most certainly was. So, the answer to the legal question - Lincoln did not have express legal authority to suspend habeas corpus, but with Congress out of session it isn't clear who else could have exercised this power in April 1861. Nothing in the Constitution said that the President could, but nothing specifically said he couldn't.

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[1] U.S. Constitution, Article 1, Section 9, Clause 2: https://constitution.congress.gov/browse/essay/artI-S9-C2-1/ALDE_00001087/

[2] Ex parte Merryman: https://www.britannica.com/event/Ex-Parte-Merryman

[3] Abraham Lincoln, July 4th Message to Congress (1861): https://millercenter.org/the-presidency/presidential-speeches/july-4-1861-july-4th-message-congress

[4] Habeas Corpus Suspension Act, 1863: https://www.loc.gov/law/help/statutes-at-large/37th-congress/session-3/c37s3ch81.pdf